Three videos of students fighting at Rolleston College were posted on the account rolly_colly_scraps which had 150 followers before it was deleted.
Sergeant Phil Bayne said police are seeking advice from its digital forensics team.
“We will then ascertain if there’s anything we can do about it. The investigation is around what the legality is and what police can do in regards to it,” he said.
Rolleston College principal Steve Saville said the school have been made aware of the account and has been communicating with police
He said two of the videos are from historic incidents and the third one happened last week.
“The incident was dealt with at the time but no action has been taken yet because we are still exploring it,” said Mr Saville.
“One of the videos is from an incident in term 1 when a student from another school came on to the grounds. That was reported quite widely at the time.”
Earlier this year a teenager disguised herself as a Rolleston College student by wearing a school jacket and entered the grounds unnoticed before attacking a 13-year-old student.