Police said they did not believe the phones of any members of the royal family had been tapped. But other public figures may have had their calls intercepted, raising potential security issues, the police said. They refused to specify who.
Police did not identify those who were arrested, but the News of the World tabloid said Clive Goodman, its royal editor, was among them.
Hayley Barlow, a spokeswoman for the Sunday newspaper, declined to comment further.
The investigation was prompted by complaints from Charles' Clarence House office to the police's royalty protection department.
"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," London's Metropolitan Police said in a statement.
Charles' office declined to comment on the arrests.
Police said they had arrested two men, a 48-year-old and a 35-year-old, at 6 a.m. and apprehended another, age 50, at 9:30 a.m. All were arrested at their homes in London under the Regulation of Investigatory Powers Act.
Police said they had searched two of the residences, along with business addresses in the Wapping, Sutton and Chelsea neighborhoods.
Anti-terrorism officers are leading the investigation and police are working with phone companies in an effort to identify all those whose conversations were tapped, they said.