An effective union would also force a newly-independent Scotland to hand over some national sovereignty, he said in a speech at a business lunch in Edinburgh.
He intervened on the technicalities for negotiations less than eight months before people in Scotland decide whether to leave the UK.
"If such deliberations ever were to happen, they would need to consider carefully what the economics of currency unions suggest are the necessary foundations for a durable union, particularly given the clear risks if these foundations are not in place," Mr Carney said.
"Those risks have been demonstrated clearly in the euro area over recent years, with sovereign debt crises, financial fragmentation and large divergences in economic performance. The euro area is now beginning to rectify its institutional shortcomings, but further, very significant steps must be taken to expand the sharing of risks and pooling of fiscal resources.
"In short, a durable, successful currency union requires some ceding of national sovereignty.
"It is likely that similar institutional arrangements would be necessary to support a monetary union between an independent Scotland and the rest of the UK."
He added: "Decisions that cede sovereignty and limit autonomy are rightly choices for elected governments and involve considerations beyond mere economics. For those considerations, others are better placed to comment."
Mr Carney, who became governor last July, focused on the implications of Scottish independence in his speech just hours after his first face-to-face meeting with Scotland's First Minister, Alex Salmond.
The pair met for private talks at Bute House, Mr Salmond's official residence in Edinburgh.
The Scottish Government wants to retain the pound if the country votes for independence, establishing a "sterling zone" with the rest of the UK. Other pro-independence groups argue for a separate Scottish currency.
Technical discussions on sharing sterling, which started under Mr Carney's predecessor Sir Mervyn King, are expected to continue.
UK ministers including Chancellor George Osborne have cast doubt on whether the arrangement is possible.
Mr Carney said any negotiations are for Westminster and Holyrood.
"Any arrangement to retain sterling in an independent Scotland would need to be negotiated between the Westminster and Scottish parliaments," he said.
"The Bank of England would implement whatever monetary arrangements were put in place."
In his speech, the governor said a currency union's success also rests on a good banking union, a term covering the range of institutions needed to support an efficient financial sector.
These include common supervisory standards, access to central bank liquidity and lender of last resort facilities.
There are difficulties separating those institutions from national fiscal arrangements, he said.
"The existing banking union between Scotland and the rest of the United Kingdom has proved durable and efficient," he said.
"Its foundations include a single prudential supervisor maintaining consistent standards of resilience, a single deposit guarantee scheme backed by the central government, and a common central bank, able to act as lender of last resort across the union, and also backed by the central government.
"These arrangements help ensure that Scotland can sustain a banking system whose collective balance sheet is substantially larger than its GDP.
"The euro area has shown the dangers of not having such arrangements, as well as the difficulties of the necessary pooling of sovereignty to build them.
"An independent Scotland would need to consider carefully how to develop arrangements with the continuing United Kingdom that are both consistent with its sovereignty and sufficient to maintain financial stability."
Mr Carney highlighted comments by the presidents of the European Council, European Commission, Eurogroup and European Central Bank, who argue that monetary union will not be complete until mechanisms are built to share fiscal sovereignty.
His speech, which was in part a lecture on the economics of currency unions, compared shared arrangements with flexible exchange rates.
Sharing a currency can in theory promote investment, reduce borrowing costs and help intergration. But it can also amplify fiscal stress and increase risks of financial instability, he said.
Having a flexible exchange rate can help absorb shocks.
"In the extreme, adverse fiscal dynamics could call into question a country's membership of the union, creating the possibility of self-fulfilling runs on bank and sovereign debt absent central bank support," he said.
But he suggested that the success, or otherwise, hinges on the mobility of labour, capital and goods; institutional structures promoting financial stability; and institutions that "mutualise risks and pool fiscal resources".
"A word of caution applies here," he said.
"There is a body of evidence that national borders can influence trade flows, even between otherwise highly integrated economies.
"The high degree of integration between Scotland and the rest of the UK may in part depend on their being part of the same sovereign nation."
Mr Carney also touched on Scotland's role in the UK's economic recovery.
"The recovery that began in Scotland has now taken hold in the UK with the economy growing at its fastest rate since 2007," he said.
"The recovery has some way to run before it would be appropriate to consider moving away from the emergency setting of monetary policy.
"The monetary policy committee has noted that, when the time eventually comes to increase interest rates, any such move would be gradual.
"That should help to reassure businesses in Scotland and all around the UK that the path of interest rates will be consistent with achieving a sustained and balanced recovery in the face of the remaining headwinds stemming from the financial crisis."
Scottish Finance Secretary John Swinney welcomed the intervention.
"Mr Carney provides a serious and sensible analysis of how a currency union can work in practice, and every one of the points he cites in terms of the technical requirements have been examined in detail by the Fiscal Commission, headed by two Nobel laureates," he said.
"We welcome the bank's commitment to further technical discussions with Scottish Government officials which will refine the work already undertaken, including the Fiscal Commission's publication of their report on a macroeconomic framework for an independent Scotland, which encompasses proposals for a shared sterling area.
"Ultimately, as Mr Carney makes clear, a sterling area is a matter for the two governments to agree. Such a shared currency area is the commonsense position as it is in the overwhelming economic interests of both Scotland and the rest of the UK.
"An independent Scotland will control 100% of our own revenues, compared to the 7% of our tax base we are currently responsible for under devolution.
"A shared currency will mean an independent Scotland having control of tax policy, employment policy, social security policy, oil and gas revenues, immigration policy and a range of other levers to suit our own circumstances, helping to grow our economy, create jobs and secure a more prosperous and fairer society."
Former chancellor Alistair Darling, who leads the Better Together campaign to keep Scotland in the UK, said the speech spells out stark problems.
"This is a detailed speech but make no mistake - the governor's judgment on currency unions is devastating for Alex Salmond's currency plans," he said.
"Why? Because the whole point of independence is to break the fiscal and political union that makes monetary union possible.
"The governor has spelled out in stark terms the problems of a currency union. Above all, it needs people living in the rest of the UK to agree to something they have never been asked about.
"As the governor makes clear, in a currency union both sides have to agree to each other's taxes, spending and borrowing. This is what is happening in the eurozone today.
"It is highly unlikely that the people living in the rest of the UK would agree to this. And remember, in a currency union like this, Scotland has 10% of GDP and the rest of the UK would have 90%. It is clear who would call the shots."
He questioned whether people in the rest of the UK would accept a banking union.
"Would people living in England, Wales and Northern Ireland agree to carry the risk of bailing out Scottish banks as they did with RBS?" he asked.
A Treasury spokesman said the Scottish Government needs a "Plan B" for currency.
"As the Chancellor has previously said, the current arrangements of a full, monetary, fiscal and political union bring economic benefits to all parts of the UK," the spokesman said.
"Governor Carney today highlights the principled difficulties of entering a currency union: losing national sovereignty, practical risks of financial instability and having to provide fiscal support to bail out another country.
"This is why the UK Government have consistently said that, in the event of independence, a currency union is highly unlikely to be agreed. The Scottish Government needs a Plan B."
Mr Carney later expanded on his comments about whether a currency area is possible.
"The Bank of England, which is a financial, technocratic institution, would implement whatever monetary arrangements were decided to the best of our ability," he said at a press conference.
"We would also, as appropriate, provide technical advice and context to those making those decisions.
"Once decisions are made, we implement. We're not the ones elected to make decisions."
He would not comment further on whether it is desirable for the bank to be lender of last resort to Scotland.
Mr Carney was also reluctant to judge whether the Scottish Government's 18-month timetable for achieving full independence is possible.
Political parties at Holyrood were able to find support in his speech for both sides of the argument.
Kenneth Gibson, the SNP convener of Holyrood's finance committee, said a sterling area is achievable.
"It is time for the UK Government to accept that common sense position, which is also backed by 71% of people in the rest of the UK," he said, citing a recent poll.
"The UK Government has already accepted the common sense position on Westminster's debt, and in light of the governor's speech there is no reason - other than trying to spread uncertainty on behalf of the No campaign - not to take the same sensible approach in relation to currency. Presumably they would wish Scotland to pay its share of the UK's debt in pounds, after all."
Scottish Conservative leader Ruth Davidson said the First Minister wants Scotland to have its cake and eat it by expected a union but retaining control over tax and spending.
"The governor of the Bank of England has blown this assertion right out of the water, leaving Alex Salmond's currency plans in tatters," she said.
"He concludes that one of the main lessons to draw from the Eurozone crisis is that to have a durable, successful currency union requires some ceding of national sovereignty."
Scottish Liberal Democrat leader Willie Rennie said: "A half in, half out version of our current union would offer Scotland the worst of all worlds.
"The SNP's independence plans would see Scotland's tax policy set by an unelected central bank operated by an another country. There would be no central lender of last resort to back up our banks and a border smack bang in the middle of our successful UK single market."