Ms Giuffre is suing the prince claiming he abused her when she was 17.
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.
Prince Andrew has consistently denied the allegations.
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.
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 said in an interview with BBC Newsnight in 2019 that he had no recollection of ever meeting Virginia Giuffre.
His lawyers had argued that Ms Giuffre agreed in court in 2009 not to sue anyone else connected to Epstein when she settled her damages claim against the billionaire sex offender.