Hampshire Constabulary said the two youngsters involved were being supported by specialist officers.
Other police forces across the UK, including in Sussex and Northamptonshire, have warned parents about a video which had been shared on various social media platforms, including Snapchat.
Hampshire police said a 25-year-old man from Stockport had been arrested in connection with the investigation and is currently in custody.
In a statement the force said: ‘Officers would like to remind people that it is an offence to hold or share such content, and if you do receive images or video content, you should delete them immediately.’
Anyone with information which could help the investigation is asked to call police on 101 quoting crime reference number 44170465274.
Further support is available on the CEOP website or by calling Childline on 0800 1111.