Thames Valley Police said earlier this month officers were considering allegations that Mountbatten-Windsor had passed documents to the late convicted sex offender, according to files released by the U.S. government.
"Thames Valley Police have opened an investigation into an offence of misconduct in public office," the force said in a statement on X.
"A man in his sixties from Norfolk has been arrested and remains in police custody. As per national guidance we will not name the arrested man."
Earlier newspapers had reported that six unmarked police cars and around eight plain clothed officers had arrived at Wood Farm on the Sandringham estate in eastern England where Mountbatten-Windsor, whose 66th birthday falls on Thursday, now lives.
The former prince, the second son of the late Queen Elizabeth, has always denied any wrongdoing in relation to Epstein, and said he regrets their friendship. But he has not responded to requests for comment since the latest release of documents.
There was no immediate comment from Buckingham Palace.
Mountbatten-Windsor had been reported to police by the anti-monarchy campaign group Republic following the release of more than 3 million pages of documents relating to Epstein, who was convicted of soliciting prostitution from a minor in 2008.
Those files suggested Mountbatten-Windsor had in 2010 forwarded to Epstein reports about Vietnam, Singapore and other places he had visited on official trips.
Thames Valley Police and the Crown Prosecution Service have previously said that they were in discussions about the case. Police said allegations of misconduct in public office, which is a 'Common Law' offence and so is not covered by written statute legislation, involved "particular complexities".
(Reporting by Sam Tabahriti and Michael Holden; Editing by Kate Holton and Janet Lawrence)

Then Britain's Prince Andrew, the Duke of York, departs after the Coronation of Britain's King Charles III and Queen Camilla at Westminster Abbey, London, Britain, 06 May 2023 (reissued 19 February 2026). According to the BBC, Andrew Mountbatten-Windsor, former titled Prince Andrew, was arrested on 19 February on suspicion of misconduct in public office. EPA/ANDY RAIN