Danny Alexander issued the warning as the Scottish Government was preparing to publish its long-awaited white paper on independence.
He claimed Treasury analysis had suggested leaving the UK could see basic rate taxpayers north of the border paying more in taxes, but the Scottish Government said Westminster has "squandered" oil revenues which could have been put in a national savings fund worth up to £22,000 for every person in Scotland.
A report by the Institute for Fiscal Studies (IFS) last week argued an independent Scotland would need to raise taxes, cut spending, or both, to create a sustainable economy over the next 50 years.
Mr Alexander has now told Scottish First Minister Alex Salmond that the IFS report is a "very stark reminder" of why Scotland should "not go it alone".
"Even under the most optimistic scenario the IFS considered, in 2021-22 an independent Scotland could have to find permanent tax increases or spending cuts that would be equivalent to £3 billion in today's terms," Mr Alexander told the SNP leader.
"This is a very stark reminder of why it is in the interest of Scotland to pool these risks, not go it alone."
Mr Alexander stated: "The IFS said it would require policy action equivalent to around an eight percentage point increase in the basic rate of income tax.
"I asked Treasury officials to look at this. They calculate than an eight percentage point rise in the basic rate of income tax would mean an average increase for basic rate taxpayers in Scotland of around £1,000 a year."
There are currently more than 2.4 million basic rate taxpayers in Scotland, who in total contribute some £6.1 billion in income tax, according to Treasury figures.
UK Government analysis shows they currently pay an average of £2,517 a year.
But the Treasury research suggested that if the basic rate of tax was increased from 20% to 28%, this would rise to £3,523 a year - an increase of just over £1,000.
In his letter to Mr Salmond, the Chief Secretary to the Treasury demanded that the white paper "must address the tax rises or spending cuts required to balance the books in an independent Scotland".
A spokesman for Scotland's Finance Secretary John Swinney said Mr Alexander's letter was "rushed and panicky" and shows "just how rattled the No campaign are by the launch of the White Paper and its positive vision for Scotland's future".
"Danny Alexander's sums are all over the place - earlier this year he was claiming independence would cost £1 per person a year, but the reality is, the policies of his Tory-led Government have cost many ordinary Scots far more than £1,000 each since they came to office," the spokesman said.
"And for Danny Alexander of all people to cite the IFS almost beggars belief. It is the failing policies of Mr Alexander and his Treasury colleagues which the IFS's forecasts are based on - forecasts which show the UK in fiscal deficit for every one of the next 50 years.
"Westminster's waste has also squandered oil revenues which could have been put in a national savings fund now worth up to £22,000 for every person in Scotland.
"Only independence will give us the chance to change things for the better, creating jobs, boosting growth and delivering a more prosperous and fairer society."