The youngster’s aunt loaded the footage onto her social media.
Portuguese press claimed the video, said to have been taken on Saturday in Paul do Mar off the south of Madeira where Cristiano Ronaldo Jr is holidaying with relatives, was also shared by his famous footballer dad and his doting grannie Dolores Aveiro before its removal.
Maritime Police chief Guerreiro Cardoso confirmed on Monday an investigation was underway.
He told respected Portuguese newspaper Expresso he was aware of what had happened and the incident was now being probed to ascertain exactly what had happened and “whether a fine had to be paid.”
He was also quoted as saying a skipper’s licence was needed to use a jet ski and only adults could hold one.
Under Portuguese law, individual fines for using a jet ski without the proper licence are understood to range between £268 and £2688.
Groups or private firms can be hit with fines of up to £10,750.
Police are understood to be trying to establish who the jet ski belonged to. The adult or adults responsible for Cristianinho, as Cristiano Jr is nicknamed by his family, would be asked to pay the fine if any wrongdoing is established.
The reaction from social media users after Juventus star Cristiano Ronaldo’s sister posted the footage on her Instagram on Sunday was immediate.
One said: “I was left with my heart in my hand when I saw the video.”