The three, aged 35, 48 and 50, were detained for "unlawful telephone interceptions" according to London's Metropolitan Police, after staff at
Clarence House reported alleged security breaches on its telephone network.
One of the three men is Clive Goodman, royal editor of Britain's best-selling newspaper, The News of the World, the newspaper confirmed.
The other two men are not journalists, though their occupations are not yet known.
The offices of News International, which owns The News of the World, have also been searched by police.
News International is the British subsidiary of media mogul Rupert Murdoch's News Corp.
A Clarence House spokesman declined to comment on the arrests.
"Police launched an investigation after concerns were reported to the Met's Royalty Protection Department by members of the Royal Household at Clarence House," a police spokeswoman said.
"It is focused on alleged repeated security breaches within telephone networks over a significant period of time and the potential impact this may have on protective security around a number of individuals."
MPs possibly affected
Police officers have not yet established how many people have been affected, and have not ruled out the possibility that other royal households could have had their phone conversations intercepted, or that the tapped conversations involved members of the Royal Family.
The investigation, which was launched more than seven months ago, has also gone beyond Clarence House to other public figures, apparently including one member of Parliament.
Television station ITV reported that other public figures who could have been affected included high-profile celebrities and Cabinet-level ministers, though not Prime Minister Tony Blair, a claim the Metropolitan Police declined to comment on.
The Press Association also said the allegations did not relate to the interception of live telephone calls, but another method of telephone interception or hacking of phones, citing unnamed sources. It added that the tapping was of mobile phones, and not land-lines.
The investigation is being handled by the Metropolitan Police's Anti-Terrorist Branch because of the security implications of the phone-tapping allegations. Officers from the Specialist Crime Directorate are also involved.
It began in December 2005 when three members of staff at Clarence House contacted the police about alleged repeated security breaches within its telephone network.