The Liberal Democrat cabinet minister predicted RBS would relocate to ensure it was "protected against the risk of collapse" as he played down SNP reassurances over a currency union.
Labour described his intervention as "very significant". However, the Scottish Government said the comments were "ridiculous" and at odds with remarks from RBS's chief executive.
In a separate move, Colin Welsh, CEO of energy investment banking firm Simmons and Co, warned the SNP's economic argument, which he said was based on the twin planks of oil and renewables, was "flawed logic".
He said: "The industry needs stability and certainty if we are to maximise the remaining reserves. We cannot afford the risk of stepping into the unknown in today's economic climate and competitive environment."
The warnings come just a day after the head of oil giant BP Bob Dudley said independence would lead to uncertainty and hit investment.
Professor Ronald MacDonald, professor of economics at Glasgow University, told MPs on the Commons Scottish Affairs Committee yesterday that a currency union could result in another Black Wednesday. He was referring to the day in 1992 when the pound was forced out of the European Exchange Rate Mechanism (ERM).
Mr MacDonald warned that if the currency arrangements were wrong it could lead to a "currency crisis".
He said: "If there was international unease about the currency arrangements within the UK then speculators, international investors, would be inclined to move assets out of the UK, which could lead to a precipitous fall in sterling with all the consequences that could have for the rest of the economy."
Speaking to MPs on the committee, Mr Cable suggested a currency union could not work and that it would be in an independent Scotland's best interests to have its own currency.
Asked about calls for the Bank of England to be an independent Scotland's "lender of last resort", Mr Cable said: "If you were managing RBS, I think you would almost certainly want to be in a domicile where your bank is protected against the risk of collapse.
"They already have a substantial amount of their management in London and I would have thought they would become a London bank, which would be symbolically quite important."
RBS was bailed out by the taxpayer to the tune of £47bn at the height of the financial crash in 2008. The bank is still 80% owned by the state.
Last year the chairman of RBS, Sir Philip Hampton, told peers the bank could leave Scotland after independence.
A spokesman for Scottish Finance Secretary John Swinney said yesterday: "Vince Cable's ridiculous comments are at odds with the common sense remarks from RBS's chief executive, who last week said that if they had to operate in 39 countries around the world rather than 38 that is exactly what they would do.
"Mr Cable has unwittingly highlighted why polls show the vast majority of people in the rest of the UK would expect the Westminster government to agree to a currency union.
"The pound is as much Scotland's as it is the rest of the UK's, and the Fiscal Commission Working Group, with experts including two Nobel Laureates, concluded it is in the interests of Scotland and the UK to continue to retain
sterling in a formal monetary union.
"As Scotland is the UK's second largest trading market, it would be absurd for Vince Cable or anyone at Westminster to stand in the way of protecting the benefits this brings to businesses and consumers in the rest of the UK."
An RBS spokesman said: "On the issue of independence we are politically neutral. We don't support political parties or political movements. We will respond to what voters decide and governments agree."
A Better Together spokesman said that Mr Welsh's comments were "absolutely devastating for the nationalists". He added: "It shows that the oil and gas industry - upon whom the SNP have based their entire case for separation - know the only way to get the best out of what is left in the North Sea is as part of the UK."
A Scottish Government spokesman said: "These claims are mistaken - the Scottish Government's economic policies for independence are based on much more than oil, gas and renewables. Major oil companies already operate across many different independent countries around the world, and an independent Scotland will be no different."