Andrew Mountbatten-Windsor, the former prince, was released Thursday evening following his arrest earlier that morning on his 66th birthday.
In a statement, the UK's Thames Valley Police said it had arrested "a man in his sixties from Norfolk on suspicion of misconduct in public office," adding it was unable to name the man "as part of national guidance."
"The arrested man has now been released under investigation," the police said in a statement later in the day.
Photos showed Mountbatten-Windsor leaving a police station Thursday evening in the back seat of a car.
Around two hours after news of the arrest broke Thursday morning, King Charles released a statement saying: "The law must take its course."
"I have learned with the deepest concern the news about Andrew Mountbatten-Windsor and suspicion of misconduct in public office," he added.
"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," he said.
The Prince and Princess of Wales are understood to be aligned with the King's statement.
Earlier on Thursday, photos showed police at the Sandringham estate in Norfolk, where Mountbatten-Windsor is said to have been living. He previously lived in Windsor, Berkshire.
The police said it was carrying out searches at addresses in Berkshire and Norfolk. On Thursday evening, police said those searches had concluded.
Mountbatten-Windsor, the brother of King Charles, was stripped of his royal titles last year amid scrutiny of his relationship with Jeffrey Epstein.
The family of Virginia Roberts Giuffre, who said she was trafficked by Epstein to have sex with the former Prince three times, also issued a statement on Thursday.
"Today, our broken hearts have been lifted by the news that no one is above the law, not even royalty," they wrote.
Andrew Mountbatten-Windsor's Epstein ties
The latest release of the Epstein files showed more of Mountbatten-Windsor's communications with the convicted sex offender.
In 2010 and 2011, when the former prince was a UK trade envoy, he appeared to forward official reports on his work visits to Epstein.
"Following a thorough assessment, we have now opened an investigation into this allegation of misconduct in public office," said Oliver Wright, assistant chief constable with the Thames Valley Police.
"It is important that we protect the integrity and objectivity of our investigation as we work with our partners to investigate this alleged offence," he added.
Before the arrest, UK Prime Minister Keir Starmer told the BBC, "Nobody is above the law."
"[The police] will conduct their own investigations, but one of the core principles in our system is that everybody is equal under the law and nobody is above the law," he said.
The last time a senior member of the royal family faced arrest or police action appears to be in 2002. Princess Anne — Mountbatten-Windsor's sister — pleaded guilty under the Dangerous Dogs Act when her English bull terrier bit two children while walking in Windsor Great Park.
