Virginia Giuffre is suing the Queen's son for allegedly sexually assaulting her when she was a teenager.
She claims she was trafficked by Epstein, the duke's former friend, to have sex with Andrew in London when she was aged 17 and a minor under US law.
The duke has denied all the allegations.
In August, when asked about the recently reported US legal action, Metropolitan Police Commissioner Dame Cressida Dick said she had asked officers to again review allegations connected to Epstein.
In a radio interview, she said "no-one is above the law" when questioned about claims of sexual assault against Andrew.
On Sunday, the Met said: "As a matter of procedure MPS officers reviewed a document released in August 2021 as part of a US civil action. This review has concluded and we are taking no further action."
The update - first reported by Channel 4 News - also confirmed the force had completed its review into allegations reported in June by the broadcaster that British socialite Ghislaine Maxwell, the late Epstein's former girlfriend, trafficked, groomed and abused women and girls in the UK.
The Met said: "We also reviewed information passed to us by a media organisation in June 2021. This review is complete and no further action will be taken."
The force said it is continuing to liaise with other law enforcement agencies who are leading the investigation into matters associated with Epstein.
The Sunday Times reported that officers had contacted Ms Giuffre, but the Met said they do not confirm who they might have spoken to as part of police inquiries.
Last week, a US judge agreed for Andrew's lawyers to receive a copy of a 2009 settlement they believe will nullify the civil case against the royal.
Epstein died while in police custody in August, 2019, in a New York jail cell, while he was awaiting trial on sex trafficking charges.
His friendship with Prince Andrew was well documented, with the duke even staying at Epstein’s home after he was convicted of sex offences.