Andrew Mountbatten-Windsor has been arrested on suspicion of misconduct in public office.
Police said he is in custody and officers are carrying out searches at addresses in Berkshire and Norfolk.
It comes after Thames Valley Police said they were assessing a complaint over the alleged sharing of confidential material by the former prince with late sex offender Jeffrey Epstein.
Andrew, who turns 66 today, has consistently and strenuously denied any wrongdoing.
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