The initial incident that led to the protest took place in Terminal 2 of the airport with a video appearing to show a male officer aiming a taser at a man as he is lying on the ground.
People are heard shouting in the background before the officer appears to kick the man’s head and bring his foot down on it.
Onlookers are told to “move back” before a female officer appears to draw her taser and aim it at other people. The male officer then walks over to another man sitting on a bench and points his taser at him, telling him to “get down”.
As the man begins to move to the ground with his arms in the air, the officer then appears to kick him.
The force said officers were called to an “altercation” between members of the public and were subjected to a “violent assault” while responding to the incident.
GMP said a police officer has since been removed from operational duties and the force has referred itself to the police watchdog, the Independent Office for Police Conduct.
A force spokesman said one of the three officers in the video had hospital treatment after suffering a broken nose with three officers in total requiring treatment.
Four men were arrested at the scene on suspicion of affray and assault on emergency workers.
A spokesman for the force said it “acknowledged concerns” surrounding the officers’ conduct and the incident was being assessed by its professional standards directorate.
Assistant Chief Constable Wasim Chaudhry said GMP understood “the immense feeling of concern and worry that people feel about our response”.
“We have already referred our actions to the Independent Office for Police Conduct and will be in further discussions with them today,” he said.
“We have spent the evening listening to community feedback and will continue to engage with communities and elected members to maintain strong partnership links and understand local views.”
Paul Waugh, the town’s newly elected Labour MP, said: “The video footage of a Greater Manchester Police officer kicking and stamping on a man in Manchester Airport is truly shocking and disturbing.
“Like many who have seen this clip, I am extremely concerned. I have had it confirmed that the man arrested is a Rochdale resident and I hope to meet the family as soon as possible.
“I have expressed my concerns directly to the Assistant Chief Constable this evening and have been in touch with Kate Green, Deputy Mayor for policing of Greater Manchester.
“It’s right that the police officer concerned has been removed from duties and that this incident has been referred to the Independent Office for Police Conduct. I expect a thorough and swift investigation.”
A GMP spokesman said: “Officers were called to reports of an altercation between members of the public in Terminal 2 at Manchester Airport.
“Whilst attempting to arrest one of the suspects of the earlier altercation, three officers were subject to a violent assault, where they were punched to the ground.
“A female officer suffered a broken nose and all three were taken to hospital for treatment.
“As the attending officers were firearms officers, there was a clear risk during this assault of their firearms being taken from them.
“Four men were arrested at the scene for affray and assault on emergency service workers.
“We acknowledge the concerns of the conduct within the video, and our professional standards directorate is assessing this.”