The allegation surfaced in a cache of legal papers unsealed by a US judge in a defamation case involving a British socialite alleged to have supplied Epstein with underage girls.
Virginia Giuffre, an alleged victim of Epstein who also claimed she was forced into a sexual encounter with Andrew, sued Ghislaine Maxwell in 2015.
In the legal documents, released on Friday, Johanna Sjoberg, another alleged Epstein victim, said Andrew touched her breast while sitting on a couch inside the billionaire’s Manhattan apartment in 2001.
Buckingham Palace said the allegations are “categorically untrue”.
In the legal papers, Sjoberg said: “I just remember someone suggesting a photo, and they told us to go get on the couch. And so Andrew and Virginia sat on the couch, and they put the puppet, the puppet on her lap.
“And so then I sat on Andrew’s lap, and I believe on my own volition, and they took the puppet’s hands and put it on Virginia’s breast, and so Andrew put his on mine.”
The legal documents claim Sjoberg was a “young college student” who was approached by “perfect stranger” Maxwell, who “lured” her to Epstein’s home with the promise of a “legitimate job”.
Giuffre’s lawyers said: “Sjoberg’s testimony also corroborates Giuffre’s account of being lent out to Prince Andrew by (Maxwell).”
Maxwell, Epstein’s former girlfriend, has denied the allegations.
A Buckingham Palace spokeswoman said: “This relates to proceedings in the United States, to which The Duke Of York is not a party. Any suggestion of impropriety with underage minors is categorically untrue.”
Epstein, 66, admitted prostituting minors in 2008 and spent 18 months in prison.
He is facing fresh charges of sex trafficking and conspiracy and could stand trial next year.