Thames Valley Police, an agency that covers areas west of London, including Andrew Mountbatten-Windsor's former home, said it was "assessing" reports that the former prince sent confidential government trade reports to convicted sex offender Jeffrey Epstein in 2010.
The assessment followed the release of millions of pages of documents connected to a US investigation of Epstein.
Mountbatten-Windsor features a number of times in the documents.
The police force on Thursday did not name Mountbatten-Windsor, as is usual under UK law.
But when asked if he had been arrested, the force pointed to a statement saying they had arrested a man in his 60s.
Mountbatten-Windsor, whose birthday is on Thursday, is 66.
"Following a thorough assessment, we have now opened an investigation into this allegation of misconduct in public office,'' the statement said.
"We understand the significant public interest in this case, and we will provide updates at the appropriate time."
Images circulated online on Thursday that appeared to show unmarked police cars at Mountbatten-Windsor's home, Wood Farm on the Sandringham Estate in Norfolk, with plain-clothes officers appearing to gather outside.
King Charles III, Mountbatten-Windsor's brother, said in a written statement: "I have learned with the deepest concern the news about Andrew Mountbatten-Windsor and suspicion of misconduct in public office.
"What now follows is the full, fair and proper process by which this issue is investigated in the appropriate manner and by the appropriate authorities.
"In this, as I have said before, they have our full and wholehearted support and co-operation.
"Let me state clearly: the law must take its course.
"As this process continues, it would not be right for me to comment further on this matter. Meanwhile, my family and I will continue in our duty and service to you all.
"Charles R."
The family of Virginia Giuffre, who alleged she was forced to have sex with the prince when she was 17 and later received an out-of-court settlement from the prince - who denied the allegations, said their "broken hearts have been lifted" after the news of Andrew Mountbatten-Windsor's arrest on suspicion of misconduct in public office.
In a statement, Sky and Amanda Roberts and Danny and Lanette Wilson, said: "At last. Today, our broken hearts have been lifted at the news that no one is above the law, not even royalty.
"On behalf of our sister, Virginia Roberts Giuffre, we extend our gratitude to the UK's Thames Valley Police for their investigation and arrest of Andrew Mountbatten-Windsor.
"He was never a prince. For survivors everywhere, Virginia did this for you."
Giuffre died by suicide in Australia last year.
Andrew is the first senior British royal in modern history to be arrested.
Mountbatten-Windsor, the second son of the late Queen Elizabeth, has always denied any wrongdoing in relation to Epstein, and said he regretted their friendship.
But he has not responded to requests for comment since the latest release of documents.
Charles stripped Andrew of his royal titles, including the right to be called a prince, in October 2025 as he tried to insulate the monarchy from the continuing revelations about his younger brother's relationship with Epstein.
Those revelations have tarnished the royal family for more than a decade.
Mountbatten-Windsor had been reported to police by the anti-monarchy campaign group Republic following the release of more than three 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.
with Reuters and PA
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