Lawyers for Virginia Giuffre filed the lawsuit in Manhattan federal court on Monday.
In a statement, Ms Giuffre said the lawsuit was brought under the Child Victims Act to allege she was trafficked to him and sexually abused by him.
Prince Andrew has always categorically denied any sexual contact or relationship with her.
“I am holding Prince Andrew accountable for what he did to me," Ms Guiffre said.
“The powerful and rich are not exempt from being held responsible for their actions. I hope that other victims will see that it is possible not to live in silence and fear, but to reclaim one’s life by speaking out and demanding justice.
“I did not come to this decision lightly," she added.
“As a mother and a wife, my family comes first — and I know that this action will subject me to further attacks by Prince Andrew and his surrogates — but I knew if I did not pursue this action, I would be letting them and victims everywhere down."
In late 2019, Prince Andrew told BBC Newsnight that he never had sex with Ms Giuffre, saying, “It didn’t happen.”
He said he has “no recollection” of ever meeting her and told an interviewer there are “a number of things that are wrong” about Ms Giuffre’s account, which alleges the encounter occurred in 2001.
“I can absolutely categorically tell you it never happened,” Prince Andrew said.
Epstein, 66, took his own life in a federal jail in Manhattan in August 2019, a month after he was arrested on sex trafficking charges.