The SNP has indicated that it would cut corporation tax to invite businesses to Scotland but Mr Brown insisted they would also be open to cutting the minimum wage at the behest of businesses.
Speaking at a campaign launch for Labour Cowdenbeath by-election candidate Alex Rowley, he urged the people of Fife and Scotland to "think carefully" before casting their vote in the referendum.
"We know that the future of Rosyth depends not only on having a Labour administration in Fife, but having us as part of the UK," he said.
"A defence centre, a nuclear centre, a renewables centre for the future.
"Fife was shaped by the mining industry, which used to have 30,000 miners, and by the Rosyth naval base and dockyard where there used be 15,000 people working but now only 1,000 people.
"We need to ensure that Rosyth has a future because Rosyth is the biggest employer in this constituency.
"It is in the defence work building the aircraft carriers, a contract awarded during the last Labour government.
"It is now in the move into nuclear and renewables, and we must support the staff.
"One of the main reasons why people in this constituency want Scotland to be part of the UK is that they know the importance to Rosyth of jobs for defence contracts throughout the whole of the UK."
Mr Brown, who also served as chancellor in Tony Blair's government, said a separate minimum wage in Scotland, England, Ireland and Wales would lead to a "race to the bottom".
He added: "Employers will say: 'We will come to Scotland if you reduce the minimum wage, or we will go to England or Wales if they cut the minimum wage'.
"So, instead of improving and sharing resources to the benefit of all people, we will end up with a race to the bottom, a dog-eat-dog competition, a devalued euro, and then all the benefits that have been built up over time will be lost.
"You don't need to look into a crystal ball to see this.
"The SNP has already announced that they wish to cut corporation tax, that they wish to compete with Ireland on corporation tax to lower the revenues that they receive.
"We don't know what effect this will have on business but we do know that there will be less money available for pensions, public services, education and health."
Mr Rowley has served as an election agent for Mr Brown, who is MP for Kirkcaldy and Cowdenbeath.
The election is being held following the death of Labour MSP Helen Eadie, who died in November last year just days after it emerged she was being treated for cancer.
Seven candidates are contesting the by-election, including the SNP's Natalie McGarry, a policy adviser working in the voluntary sector, local councillor Dave Dempsey, who is standing as the Conservative candidate, and IT worker Jade Holden, who has been selected for the Liberal Democrats.
Both the SNP and the Conservatives are expected to officially launch their campaigns on Friday.
Mr Rowley said: "It was with shock and sadness that I learned of the sudden death of Helen Eadie, and over the last few weeks as we have gone around the doorsteps people right across the constituency are also expressing their deep sadness and saying how much of a good MSP she was.
"People have questions about independence and concerns that these questions are not being answered.
"People have concerns about jobs and to ensure that young people have opportunities for the future with high-quality public services.
"None of that would be guaranteed in an independent Scotland."
The SNP has accused Mr Rowley of favouring a rise in the council tax, which has been frozen since the SNP came to power in Holyrood, and insist Labour's review of public services will favour an end to universal services such as free prescriptions.
Mr Rowley said: "I have said time and time again that there will be no increase in the council tax.
"The council tax freeze is there to 2016, and after 2016 we need a vision for local government on how we are going to fund it and what role it must have in Scotland.
"In terms of free prescriptions, they are there and we will not campaign to take them away."
Scottish Labour leader Johann Lamont confirmed that her party will set out the findings of their devolution commission at their party conference in March.
Mr Brown is also expected to return to Fife this Saturday to talk about the advantages of continued devolution.
Ms Lamont said: "Labour has a devolution commission. We will report in March at our conference and we will be making clear then how we believe we can strengthen devolution.
"We have two messages in that. One, that this is not argument for power for power's sake, but what you can do with the power that you have got.
"Our frustration is that the Scottish Government has the power to make a difference on the bedroom tax, childcare, education and health, but they have put that on pause because of their party obsession with separating Scotland off from the rest of the UK.
"We were told that childcare was the Scottish Government's first priority, that the reason they wanted independence was childcare.
"We supported their pledge for 50% of two-year-olds to have childcare and they voted that down. They chose to spend the money instead on free school meals.
"These are all good things but it's about choices. Childcare is critically important but the SNP chose to spend the money on something else."
SNP MSP Annabelle Ewing described Mr Brown's comments as "hypocritical nonsense".
"His remarks entirely ignore the fact that the UK has become a much more unequal society under successive Westminster governments, Tory and Labour, which is one reason why stalwarts of the Labour movement in Scotland such as Charles Gray, Alex Mosson, Lorna Binnie and John Mulvey are voting Yes in September," he said.
"If Mr Brown cannot even convince highly-respected Labour figures in Scotland to vote No, then the Tory-led No campaign will not persuade the majority of the Scottish electorate.
"With jobs at Rosyth having declined by 55% under Labour's watch, it is his party and the Westminster system that have well and truly let the area down.
"A UK Government also closed the naval base, preferring to prioritising defence jobs in the south of England.
"As the Scottish Government's white paper makes clear, Rosyth has a bright future in an independent Scotland, including military procurement, and its successful record in the global market place in a range of areas such as offshore energy and marine services.
"Scotland's Future also makes clear that after a Yes vote the minimum wage in an independent Scotland will rise with at least the cost of living, helping people in Scotland with the rising cost of living that the Westminster system has utterly failed to tackle.
"With Gordon Brown having previously called for the power for different regions to set their own minimum wage, his remarks today are nothing short of hypocritical in the extreme.
"What Gordon Brown is saying is that vital social provisions such as welfare and the minimum wage are better decided by Tories at Westminster rather than in Scotland's own parliament, a position very out of touch with opinion in Cowdenbeath constituency."