Some 51% said the blueprint, launched in a blaze of publicity last month, would make no difference to how they would vote in the referendum next year.
One in five said the SNP's detailed proposals have made them more likely to vote against independence in next year's referendum.
Slightly fewer, 18%, said they were more likely to vote Yes as a result of the White Paper.
The findings, in an Ipsos Mori poll of more than 1000 voters conducted in the week after the document's launch, will come as a blow to the SNP and the Yes Scotland campaign.
In the run-up to its publication, Deputy First Minister Nicola Sturgeon said the 670-page White Paper contained "all the answers" about independence and campaigners saw it as a potential "game-changer" in the debate.
The poll's headline finding, using the question that will be posed next September, put support for Yes at 34% and backing for No at 57% among those certain to vote.
One in 10 was undecided. Support for Yes was up slightly, while backing for No fell compared with Ipsos Mori's September survey.
The pro-independence Yes Scotland campaign said its own research suggested opinion polls had yet to "catch up with the campaign". A spokesman added: "This debate has a long way to go and we at Yes Scotland are under no delusions about the hard work that needs to be done to secure the votes from those 'undecideds'. We are confident we will deliver a positive Yes result in September 2014."
Blair McDougall, of the pro-UK Better Together campaign, said: "Despite spending hundreds of thousands of pounds of taxpayers' money on their White Paper manifesto, the number of people saying they support Alex Salmond's plan to break up the United Kingdom is actually lower than it was before they started their campaign. "