Andrew Mountbatten-Windsor has been arrested on suspicion of misconduct in public office.
Thames Valley Police confirmed it had arrested a man in his 60s in Norfolk on Thursday and was carrying out searches at addresses in Berkshire and Norfolk. He remains in custody, it said.
What are believed to be unmarked police cars were seen on Thursday morning at Sandringham – the King’s Norfolk estate, where the former prince has been living since leaving his home in Windsor, in Berkshire.
Police had previously said they were considering investigating Andrew over allegations relating to his association with the late sex offender Jeffrey Epstein.
They were reviewing allegations Andrew shared confidential material with the disgraced financier, after communications between the two were amongs files released by the US government.
This is the first time Andrew has been arrested. He has consistently and strenuously denied any wrongdoing.
Thames Valley Police said that, following a “thorough assessment”, a formal investigation had now been opened.
It also said earlier in February that it was assessing a separate allegation that a second woman was sent to the UK by Epstein for a sexual encounter with Andrew in 2010. The woman, who is not British, was in her 20s at the time.
Thursday’s arrest is not in relation to any allegations of sexual offences.
Thames Valley Police said it was not naming the arrested man “as per national guidance”, and warned that as the case was now active, care must be taken to avoid being in contempt of court.
Assistant Chief Constable Oliver Wright said: “We understand the significant public interest in this case, and we will provide updates at the appropriate time.”
Norfolk Constabulary told the BBC it was “supporting a Thames Valley Police investigation into misconduct in a public office”.
The former Duke of York served as the UK’s trade envoy between 2001 and 2011, travellig globally and enjoying privileged access to senior government and business contacts around the world.
In 2010, Andrew appears to have forwarded government reports from visits to Vietnam, Singapore and China to Epstein, files relating to the late financier recently released by the US Department of Justice appear to show.
The documents also appear to show Andrew forwarded information on investment opportunities in gold and uranium in Afghanistan to Epstein.
Under official guidance, trade envoys have a duty of confidentiality over sensitive, commercial, or political information about their official visits.
Andrew has always denied any wrongdoing over his association with Epstein. He has not responded to the BBC’s requests for comment on the specific allegations in relation to the release of millions of Epstein files in January.
The former prince previously faced allegations from a first woman, which were settled out of court.
His accuser, Virginia Giuffre, alleged she was made to have sex with Andrew on a number of occasions, including on Epstein’s private island Little St James in the early 2000s.
The settlement reached between the two made no admission of wrongdoing on Andrew’s part.