The incident, which has been previously reported and Andrew has denied, was among the details revealed in a trove of previously redacted documents.
Epstein socialised with Wall Street titans, royalty and celebrities before pleading guilty to soliciting prostitution from a minor in 2008. He took his own life in 2019 at age 66 while awaiting trial on federal sex-trafficking charges.
The names of more than 150 people mentioned in a lawsuit by Virginia Giuffre, one of Epstein's most prominent accusers, were kept under seal for years until a federal judge ruled last month that there was no legal justification to keep them private.
In a deposition, Giuffre said she had sex with several prominent politicians and financial leaders, including billionaire US businessman Tom Pritzker.
Pritzker did not immediately respond to a request for comment. Giuffre did not say whether she was underage at the time or whether the sex was nonconsensual.
Giuffre's allegation against Pritzker appeared to be previously unreported.
In her deposition, she also said she had sex with other prominent figures who have previously denied her allegations, including hedge-fund owner Glenn Dubin, former US senator George Mitchell and former New Mexico Governor Bill Richardson.
In a separate deposition, Epstein accuser Johanna Sjoberg said Prince Andrew put his hand on her breast to pose for a photo with Epstein, Giuffre and Ghislaine Maxwell, Epstein's former girlfriend.
Sjoberg said the photo also included a puppet that said "Prince Andrew" on it.
Andrew has been stripped of most of his royal titles due to his association with Epstein. He settled a civil lawsuit with Giuffre last year for an undisclosed sum and has denied wrongdoing. He was not immediately reachable for comment.
The list stems from a long-settled defamation lawsuit that Giuffre filed against Maxwell.
Maxwell, the daughter of British media mogul Robert Maxwell, is serving a 20-year prison sentence for recruiting underage girls for Epstein. She is appealing her conviction.
Giuffre accused Maxwell of recruiting her when she was underage for Epstein to abuse.
US Judge Loretta Preska, who is overseeing the case, ruled that some names would remain confidential, including those of people who were underage when Epstein abused them.