Mr Brown said a Yes vote for independence would mean the loss of the “pooling and sharing” of resources which help pay for state pensions and other benefits for retired people.
He said he did not believe the SNP administration’s assertions that pensions would continue to be paid, pointing to questions over the value of North Sea oil revenues in the coming years.
The Kirkcaldy and Cowdenbeath Labour MP said the issue presented the third major problem for Scottish First Minister Alex Salmond, following debates surrounding an independent Scotland’s entry into the EU and the prospects of forming a formal currency union with the rest of the UK.
Mr Brown was speaking to an audience of pensioners at an event in Lochgelly, Fife, to launch the campaign group Keep our British Pensions.
He said: “We know when we look at the figures for pensions, we in Scotland get a higher share of the UK pension money.”
Mr Brown said that when benefits such as pensioners’ credit, the winter fuel allowance and free television licences are added to the state pension, Scots receive around £200 more on average each year than their English counterparts - amounting to £200 million in total for the country.
‘Scotland has more pensioners, therefore we get more’
He said: “Why does that happen? It happens because we pool all of our resources as part of the United Kingdom.
“We pay our national insurance and we pay our taxes so that we can pay for our pensions later.
“We have more needs (in Scotland) and more pensioners, therefore we get more.”
Mr Brown continued: “The SNP know that they have got a problem... the rising demand for pensions, set against the money that they have, means there is greater volatility in social security spending.”
“They haven’t answered the basic problem - you have paid into your pension, into the UK Exchequer all your lives, you’ve paid your national insurance, you’ve paid your taxes so that you have a right to a pension.
“You are expecting, quite rightly, that you will get a British pension - but if there is independence, the British pension stops, the national insurance fund that you’re paying into is broken up.
“There will be a separate Scottish national insurance fund, and the rest of the UK will have the lion’s share.”
Mr Brown argued that the SNP’s estimates for oil revenues - which would help fund pensions under independence - were at odds with private documents leaked to the media.
“They didn’t expect to get £6.9 billion from oil, they only expect to get £4 billion...far from having all these billions of resources, the SNP are exaggerating all the time.
“That difference of over two million is the equivalent of half the amount of money spent on everybody’s pension in Scotland.
“If that money is not there, how are pensions going to be afforded?”
‘Leaving UK means leaving security of pensions system’
Mr Brown was joined at the Fife launch by Gregg McClymont, Labour’s shadow pensions minister.
Mr McClymont said leaving the UK means leaving the “certainty and security” of the pension system.
He said Scots would no longer benefit from the UK Government’s protection fund which helps to safeguard against the loss of private pensions.
In the past, he said, some workers would have been left “high and dry” without this UK-wide “lifeboat based on pooling and sharing resources”.
The SNP described Mr Brown’s comments as “scaremongering”.
Deputy First Minister and SNP depute leader Nicola Sturgeon said: “The last person anyone in Scotland will take lessons from when it comes to pensions is Gordon Brown - the man who destroyed final-salary pension schemes with his £100 billion raid, and insulted our older folk with a miserly 75p increase in the state pension.
“Mr Brown’s track record means that he lacks all credibility on this subject, so it is little wonder that his speech bears little relationship with reality.
“The Scottish Government has set out clearly and unambiguously that people will continue to receive the pension entitlements they have built up - and any attempt to insinuate otherwise is grossly irresponsible.
“Social protection costs represent a lower share of tax revenues in Scotland than for the UK as a whole - meaning pensions are more affordable for Scotland - and academic surveys and polls consistently show that people want decisions on pensions and welfare to be made in the Scottish Parliament rather than by Westminster.
Ms Sturgeon said National Institute of Economic Research showed that pensions in Scotland would be 6 per cent to 8 per cent cheaper than in the rest of the UK.
“Where Westminster has decimated pension schemes and is rushing ahead an accelerated timetable that will see the retirement age rise rapidly, a Yes vote in September will ensure we have a pensions system that is right for Scotland,” she said.