The peer, who was sacked as US ambassador last year because of his links to Epstein, featured in documents released by the US Department of Justice on Friday related to the pedophile financier.
Lord Mandelson said he had written to Labour Party General Secretary Hollie Ridley to say he was stepping down from his party membership.
"I have been further linked this weekend to the understandable furore surrounding Jeffrey Epstein and I feel regretful and sorry about this," he wrote.
"Allegations which I believe to be false that he made financial payments to me 20 years ago, and of which I have no record or recollection, need investigating by me.
"While doing this I do not wish to cause further embarrassment to the Labour Party and I am therefore stepping down from membership of the party," he said.
Lord Mandelson features in several bank statements released on Friday - totalling $US75,000 ($A107,800) - in the huge tranche of files related to the financier released by the US government.
In one bank statement, a payment of $US25,000 ($A36,000) to the account of Reinaldo Avila da Silva, now Lord Mandelson's husband, features on May 14, 2003.
The statement appears to describe "Peter Mandelson" as the beneficiary of the payment.
Two statements from May and June 2004 also feature $US25,000 payments to Lord Mandelson, one to an account which appears in his name and another in which he appears to be listed as a beneficiary.
Lord Mandelson told the BBC he had no recollection of receiving the payments, and did not know if the documents were genuine.
Other disclosures from the latest Epstein files show a man who appears to be Lord Mandelson in a series of undated photographs, stood in his underwear and a T-shirt alongside a woman whose face has been hidden.
The peer told the BBC he "cannot place the location or the woman and I cannot think what the circumstances were".
Elsewhere, the files appeared to show da Silva was transferred thousands of pounds by Epstein to pay for a fee so he could attend the British School of Osteopathy.
Lord Mandelson has previously offered an unequivocal apology to Epstein's victims.
He has also insisted he had "nothing more to add" on his links to Epstein.
Being pictured or mentioned in the Epstein files is not an indicator of any wrongdoing.
