'The Sun' newspaper reported that it was offered the images of the British royal family by someone asking for 50,000 pounds within 48 hours.
The photographs of Prince George and Princess Charlotte are believed to be among those that have been hacked from their aunt Pippa Middleton's iCloud account.
"Police have received a report concerning the alleged hacking of a personal iCloud account. Specialist officers are now investigating," Metropolitan Police said in a statement.
A spokesperson for Pippa said: "Thank you very much for drawing this to the family's attention. I can confirm that not only have the lawyers been informed but the police are about to be involved as well."
Pippa was maid of honour when the Duchess of Cambridge married Prince William in 2011.
Earlier this year, she and her boyfriend, hedge fund manager James Matthews, confirmed they are engaged to be married, with a wedding planned for next year.