Virginia Giuffre is suing the prince, claiming he abused her in 2001.
His lawyers said the case should be thrown out, citing a 2009 deal she signed with convicted sex offender Jeffrey Epstein. But a New York judge ruled that the claim could be heard.
He has consistently denied the claims. Buckingham Palace said it would not comment on an ongoing legal matter.
The motion to dismiss the lawsuit was outlined in a 46-page decision by Judge Lewis A Kaplan of the United States District Court for the Southern District of New York.
It means the case against the Duke of York, 61, could be heard later this year.
In court documents, Ms Giuffre said she was the victim of sex trafficking and abuse by late billionaire financier Epstein.
Part of her abuse involved being lent out to other powerful men, she alleges.
Prince Andrew, the Queen's second son, said in an interview with BBC Newsnight in 2019 that he had no recollection of ever meeting Virginia Giuffre, and her account of them having sex "didn't happen".
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