It is understood that a pro-independence activist accused the SNP of fundraising to press for a second poll but allegedly spending the cash elsewhere.
Officers have been ordered to assess the allegations before any decision is made to formally investigate.
A Police Scotland spokesperson said: “We received an allegation of fraud around 4.40pm on Thursday 25 March 2021.
“Enquiries are ongoing and at an early stage.”
Details of the claim emerged days after First Minister Nicola Sturgeon admitted it was 'not appropriate' for two SNP branches to apply for £20,000 in coronavirus support cash.
However, The SNP insist the fraud claim was part of a 'dirty tricks campaign' and 'utterly baseless'.
The party also denied claims made on a pro-independence blog that Ms Sturgeon and her husband Peter Murrell, the SNP's chief executive, had been interviewed by police.
According to The Mail on Sunday, three senior officials resigned from the SNP's finance and audit committee during a meeting of the party's governing body last month.
Edinburgh Lord Provost Frank Ross, Allison Graham, of Mid Scotland and Fife; and Cynthia Guthrie, a company director, had asked to see the full accounts and resigned when Mr Murrell refused.
Ms Guthrie is now standing for election next month as a candidate for Alex Salmond's Alba Party in the South of Scotland.
Opposition parties accused the SNP of failing to focus on the post-Covid economic recovery.
Scottish Tory chief whip Miles Briggs said: “While we remain entirely focused on blocking a divisive independence referendum and building back from the pandemic, the Nationalists are at war with each other.
“Nicola Sturgeon's SNP are no longer content with dividing our country, as they turn on one other with increasing venom.
“These serious allegations of fraud must be fully investigated, without fear or favour, to establish if there has been any criminality.”
Scottish Labour's deputy leader Jackie Baillie said: “The departure of three members of the SNP's finance committee last month rightly raised questions.
“This is a concerning development which requires swift answers.”
Alistair Carmichael MP, election campaign chief for the Scottish Liberal Democrats, told the newspaper: “This is the latest story that shows something rotten in the state of the SNP.
“They need to be removed and replaced by parties like the Liberal Democrats, who will put recovery first.”
An SNP spokesperson said: “There have been attempts by opponents of the SNP to stir this up for some time. It is part of an ongoing dirty tricks campaign and like most conspiracy theories, it is utterly baseless.
“The SNP has no knowledge of any investigation but will be more than happy to set out the facts should questions be asked of us by any appropriate authority .
“The money has helped us set up an Independence Unit, make other preparations, and budget for £600,000 of independence-related campaigning in the year ahead.”