Vehicles were seen arriving at Sandringham Estate in Norfolk on Thursday (19 February), where Andrew Mountbatten-Windsor has been living, as he was arrested.
Mr Mountbatten-Windsor was arrested on suspicion of misconduct in public office.
In a statement, police said officers were carrying out searches at addresses in Berkshire and Norfolk. They added that the arrested man remains in police custody.
The 66-year-old has been living at Wood Farm, a cottage on the estate, after leaving the Royal Lodge in Windsor.