The brutal, nine-minute-long video posted on the internet shows one man handcuffed in the back of a ute being beaten with rods, while another man is on the ground being tugged at by a dog.
Human rights groups have accused the Fiji military of carrying out the assaults on the men, and the Fiji police say they are investigating.
Speaking to media during his trade trip to Mexico, Mr Key said the video was "alarming and concerning" and Foreign Minister Murray McCully would raise it with his Fijian counterpart.
"We expect the Fijian authorities to deal with them appropriately and hold those people who have undertaken those beatings to account. It's the sort of thing we worry an awful lot about."
He said New Zealand was also concerned about Fiji's progress towards the election promised for 2014 after the Fiji government overrode many of the recommendations of the independent Constitutional Commission it had set up, including requiring political parties to have 5000 members to contest the election.
"We have real concerns about the constitutional changes that have been recommended. We were firmly of the view that [Commission chair] Professor Yash Ghai's recommendations were more in the right line, but we are dealing with reality on the ground in Fiji and it's not perfection but let's see how things go."
Mr Key said if Fiji could reach a point where democracy was possible it would be pleasing "but let's see the conditions under which parties are ultimately able to participate".
Fiji police Inspector Atunaisa Sokomuri, speaking on behalf of the Commissioner of Police, said a thorough investigation to establish the circumstances of the incident has been ordered.
"We want to stress from the outset that no-one should prejudice this investigation by speculating on what happened. We need to formally establish the precise facts and we are determined to do so," Fijilive reported him as saying.
He said some reporting on the video had been incorrect, and police had established the men in the video were not prisoners who had escaped from Naboro last year.
Police were not prepared to speculate on the identities of those involved, so as not to prejudice the investigation.
Mr Sokomuri said the procedures of the police investigation would be similar to those when complaints against police were lodged in countries like Australia and New Zealand.
The video has appalled human rights activists here, who are calling on the Government to lean on the interim Fiji Government to take action over the video.
Human rights campaigner and lawyer Peter Williams QC said New Zealand aid could be withheld from Fiji if no charges were brought against the perpetrators of the alleged torture and beatings.
"I think we're waiting in New Zealand to see what the authorities are going to do about it. If no charges are brought then I think the New Zealand Government should bring some pressure on the dictatorship over there, the military government, to do something about it."
The video showed "shocking brutality", Mr Williams said.
Amnesty International executive director Grant Bayldon said they had a team in London working on verifying the video.
He said the humiliation of the men, and their injuries, were "very serious".
"Forced to undress and harassed by a dog, as men nearby laugh, it is difficult to watch. The subsequent brutal beating with batons is harrowing. It is torture."
The video showed the beatings being administered by plain-clothed men speaking Bauan - a Fijian dialect.
It was thought the footage was from an incident last year where five prison escapees were apparently assaulted by the military when the inmates were eventually recaptured.
- Claire Trevett of the NZ Herald and APNZ staff
