The pictures were reported by The Sun and Daily Mail newspapers to have been stolen from Middleton's iCloud account and included shots of her sister Kate, plus her and William's children Prince George, three, and Princess Charlotte, one.Someone had been in touch with media via the encrypted messaging service WhatsApp to offer them for sale, the reports added.
The Sun said it had been asked for £50,000 (58,000 euros, $65,000) for the shots.
Scotland Yard police headquarters said they had received a report on Friday concerning the alleged hacking of a personal iCloud account and specialist officers were investigating.
On Saturday, a 35-year-old man was arrested at an address in Northamptonshire, central England, they said.
"He was arrested on suspicion of a Computer Misuse Act offence and is being taken into custody at south London police station," a statement said.
"Enquiries continue."
Pippa Middleton, 33, is the younger sister of Kate and found fame after acting as bridesmaid at her sister's wedding to William in 2011.
She is engaged to hedge fund boss James Matthews and the couple are expected to get married next year. The allegedly hacked photos also reportedly included shots of her own wedding preparations.
William and Kate and their children were due to start an eight-day tour of western Canada on Saturday.
The Duke and Duchess of Cambridge are set to view spectacular nature sites and meet with refugees and indigenous Americans during the visit.
William's grandmother Queen Elizabeth II is Canada's head of state and he is second in line to the throne.
