It was revealed in an FBI document, released as part of the US Department of Justice's document dump related to Epstein, that the woman went to Epstein's home in New York and Andrew was in the kitchen.
The woman, who grew up in Brazil, told the FBI that she was "quite shocked to see him".
The woman, whose name has been redacted in the document dated December 2020, told the FBI how Epstein "pushed her against the wall trying to take her top off" in another room after the massages, in which everyone was fully-clothed.
It is not clear when the incident is said to have happened.
It comes after one photo in a separate document in the Epstein files appears to show Andrew touching a fully-clothed woman's abdomen.
The woman told the FBI in the document how she first met Epstein and described being abused by him.
She went on to describe going to Epstein's home in New York and how, after massaging the former duke's back, he massaged her back, shoulders, waist, and hands.
The document says: "(Redacted) went to Epstein's home in New York and he took her to the kitchen. Prince Andrew was in the kitchen with another girl. (Redacted) recognised Prince Andrew and was quite shocked to see him.
"(Redacted) described the girl as being approximately 20 something and able to speak good English but not an American.
"Epstein told his Prince Andrew that (redacted) was good at massages.
"Epstein asked (redacted) to massage Prince Andrew's shoulders and back.
"(Redacted) started massaging Prince Andrew's back. Epstein left the room and came back to the room with a camera.
"Prince Andrew then told (redacted) it was her turn to be massaged. Prince Andrew massaged (redacted) back, shoulders, waist, and hands."
The document adds: "Everyone had clothes on during these massages. (Redacted) just wanted to leave. Epstein then told (redacted) to come with him and he took her to a different room from the room where Prince Andrew and the girl was in; Epstein then pushed her against the wall trying to take her top off.
"Epstein told (redacted) he wanted to take a picture of her.
"(Redacted) told him he could take a picture but she would not let him take her top off.
"Epstein asked (redacted) about her marriage and told her she could do well in London.
"Epstein told her that marriage could be boring and they could do things together."
It comes after the former duke was arrested last month on suspicion of misconduct in public office following allegations he shared sensitive information with the paedophile financier while serving as the UK's trade envoy.
Andrew has denied any wrongdoing over his links to the convicted sex offender, but has not directly responded to the latest allegations.
He spent around 11 hours in custody in February as searches were conducted at his home on the Sandringham Estate in Norfolk and at his former home, Royal Lodge in Windsor, Berkshire, and was released pending investigation.
Andrew served as the UK's special representative for international trade and investment from 2001 until 2011, when he stepped down amid controversy over his friendship with Epstein.
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