The Lib Dem Chief Secretary to the Treasury said that the amount was the same as the combined annual budgets of Police Scotland and the Scottish Fire and Rescue Service.
And he warned that Scottish ministers would have to raise taxes or cut spending to make up for the missing money.
The figure covers just three of the policy commitments contained in the document.
Last night the Scottish Government hit back, saying that Mr Alexander's figures were "all over the place".
The analysis will be published in full by the Treasury later today.
It looks at commitments to provide 1140 hours of childcare a year to all children from the age of one until they reach school age, a 50% cut in Air Passenger Duty, and a 3% cut in corporation tax.
The Treasury said that Scottish ministers had provided insufficient detail to allow it to cost a range of other pledges in last month's White Paper.
These include a potential reduction in the state pension age and the return of the Royal Mail in Scotland to public ownership.
Mr Alexander said: "This detailed Treasury analysis shows the Scottish Government would need to find £1.6 billion a year in higher taxes or spending cuts to fund just some of the additional commitments set out in the White Paper. The reality is that the White Paper shows nothing about how they would pay for these commitments."
Mr Alexander said the Scottish Government "cannot claim it is going to spend what it will not have".
He said: "Within the UK, Scottish businesses are benefitting from the substantial cuts in corporation tax the Coalition has delivered, and Scottish families will benefit from tax-free childcare in 2015.
"Both of these policies bring big benefits to Scotland at no cost to the Scottish Government budget - proving once again how well the UK works for Scotland."
The Scottish Government accused the Treasury of getting its sums wrong. Deputy First Minister Nicola Sturgeon said: "Danny Alexander's figures are all over the place.
"In September, the No campaign were claiming a funding gap of £32 billion.
"By last month that had shrunk to £10 billion, and now they are saying it is £1.6 billion - all these figures are wrong, but at this rate even the No campaign will be predicting a healthy surplus by the time the referendum arrives."
She added that the analysis did not take into account the impact of the policies designed to boost the economy.
The Scottish Government estimates that a 3% reduction in corporation tax will boost employment by 27,000 jobs.
Ministers also believe the introduction of their child care policy will increase the number of women in the workplace, who in turn will pay more in tax.