Detectives investigating the hacking arrested a 35-year-old man in Northamptonshire in central England, police said.
The man was arrested on suspicion of a Computer Misuse Act offense, and he is now in custody at the south London police station, the Met Police said.
Images of Kate Middleton and her children, Prince George and Princess Charlotte, were reportedly among some 3,000 images stolen when the account was hacked, according to Britain's Press Association news agency.