The incident occurred during the arrest of a man, 34, in Porthmadog, Gwynedd, north west Wales, on Wednesday.
In the footage, a male officer is seen with his arm around the man's neck appearing to punch him in the face.
North Wales Police said the matter was being "fully investigated" and referred itself to the police watchdog.
The Independent Office for Police Conduct (IOPC) has since launched an independent investigation.
The video appears to show the suspect taken to the ground by a male and female officer after a brief altercation.
Separate footage shows the man being led to a police vehicle with a swollen and bruised face.
He was then taken to hospital and assessed by medical staff before being transferred into police custody, said the force.
The incident happened on Pensyflog, a street in the coastal town of Porthmadog.
Nia Jeffreys, Gwynedd councillor for the area, said: "The whole community is shocked to tell the truth and it's really shaken our faith and trust in the police here in north Wales.
"Trust is definitely shaken. Nobody expects to see one police officer punching a man several times whilst he is already on the floor, it's very serious.
"This kind of behaviour by one police officer can't be tolerated it's very difficult to justify."
Ms Jeffreys added that she, along with the local MP and MS, have written to the chief constable to determine the "facts of this situation".
Police and Crime Commissioner for north Wales, Andy Dunbobbin, described the footage as "concerning" and said he was taking it "very seriously".
"I discussed this incident with the chief constable this morning and she has confirmed the matter is rightly being investigated by North Wales Police," he said.
"I take such incidents very seriously and will work with the police and other bodies to understand the circumstances behind the footage," he added.
David Ford, director of the IOPC, said: "Footage on social media, capturing part of the interaction between police officers and the arrested man has, understandably, attracted significant interest and public concern.
"It is important that we thoroughly and independently investigate the whole incident, in order to establish whether the level of force used during the arrest was reasonable and proportionate in the circumstances."
A North Wales Police spokesperson said: "This matter is currently being fully investigated by North Wales Police and further updates will be issued in due course."