One posting of the video on YouTube said it showed the torture last year of recaptured prison escapees.
In the video, one man on the back of a ute is beaten repeatedly with wooden and metal poles and then stripped of his underwear and further attacked.
Another man on the ground is also hit and dragged by a dog.
Police said they had launched a thorough investigation into the circumstances surrounding the incident.
"We want to stress from the outset that no-one should prejudice this investigation by speculating on what happened," police said in a statement.
"We need to formally establish the precise facts and we are determined to do so."
Fiji police criticised international reporting on the incident, saying that some of it had been wrong.
Amnesty International said it was working to verify the contents of the video.
Grant Bayldon from Amnesty New Zealand said the violence shown appears to be consistent with the assault and torture of recaptured prisoners that the human rights organisation documented in December.
"To say categorically who committed the attacks is not something Amnesty can do, the Fiji Government needs to investigate," he said.
Fiji police denied the men were prisoners who escaped from Naboro Minimum Security prison in December.
"These crimes were perpetrated by a group of criminals with impunity and who had absolutely no regard for lives of ordinary Fijians, respect for basic human dignity and the law," police said.
"That said, what is on the video requires investigation. The procedure of investigation we will follow is similar to those followed when complaints have been lodged against police officers in other jurisdictions."
The ABC has approached the interim government for comment.
Anti-regime website Coupfourpointfive said one of the beaten men later had to have part of his right leg amputated.
It said the video highlights police and military brutality.