A woman named him in documents she filed in a Florida court over how prosecutors handled a case against financier Jeffrey Epstein.
She claims that between 1999 and 2002 she was forced by Epstein to have sex with the prince when she was a minor.
The palace said it would not comment in detail on the legal proceedings.
But a Buckingham Palace spokeswoman said: "This relates to long-standing and ongoing civil proceedings in the United States, to which the Duke of York is not a party.
"As such we would not comment on the detail. However, for the avoidance of doubt, any suggestion of impropriety with under age minors is categorically untrue".
The woman says she was forced to have sexual relations with the prince in London, New York and on a private Caribbean island owned by Epstein.
The accusation is contained in a motion filed in a Florida court this week, which is part of a lawsuit over how federal prosecutors handled the case of Epstein.
The court document, first reported on by Politico Magazine, alleges: "Epstein also sexually trafficked the then-minor Jane Doe (a name used in US legal proceedings for people with anonymity), making her available for sex to politically connected and financially powerful people.
"Epstein's purposes in 'lending' Jane Doe (along with other young girls) to such powerful people were to ingratiate himself with them for business, personal, political, and financial gain, as well as to obtain potential blackmail information."
Prince Andrew is one of three well-known men named in the court document who it alleges had sexual relations with the woman.
BBC royal correspondent Peter Hunt said the documents related to "a long-running, complicated legal action which began in 2011".
"What these court documents do which hasn't been done before is that an unnamed woman alleges she was forced to have sexual relations with Prince Andrew when she was a minor, three times in three different locations," he added.
The prince has previously been criticised for his former friendship with Epstein, who was convicted of sex offences in 2008.
The pair were photographed meeting in December 2010, after the tycoon had served an 18-month prison sentence for soliciting a minor for prostitution, and the prince had also visited Epstein at his Florida home over the years.
The prince stepped down as the UK special representative for trade and investment in July 2011 after 10 years in the role.
From the Independent
Reports in the US media say many of the A-list celebrities broke off any links with the former maths teacher after his arrest and conviction of having sex with an underage girl whom he had solicited. His arrest followed an 11-month undercover investigation at a Florida mansion that Epstein used.
In 2008, he pleaded guilty to a single charge of soliciting prostitution and was handed a 18-month jail sentence. He served 13 months in jail and was obliged to register as a sex offender. A 2011 report in the New York Post said that he celebrated his release from jail and his return to a property he maintains in New York with Prince Andrew.
The Independent names Kevin Spacey and Chris Tucker as having received free flights to Africa on Epstein's jet. It makes no claim that either were involved in sexual escapades arranged by Epstein. Nor does it claim that Bill Clinton was involved in 'sexcapades' with Epstein, but it does say that -
Bill Clinton flew on multiple occasions to Epstein’s private Caribbean island between 2002 and 2005 as he developed his philanthropic post-presidential career.
According to the Guardian, the document alleges:
Between 1999 and 2002, the woman and three others were repeatedly sexually abused by Epstein, who also “loaned her out” to other rich and famous men.
The men named include Prince Andrew and Alan Dershowitz, a Harvard law professor. But they are not named as parties to the claim, meaning that have been unable to respond to it.
The woman making claims against Prince Andrew was 17 at the time. She is known as Jane Doe 3 in the document and asked the Guardian to stay anonymous
She claims to have met Epstein when she was approached by Ghislaine Maxwell, the daughter of Robert Maxwell and Epstein’s close friend.
Maxwell is then alleged to have helped Epstein convert the girl into a “sex slave”, abusing her in a number of international locations.