Demonstrators took to the streets on Friday carrying “Black Lives Matter" banners, after the video was shared on social media.
Footage shows an officer detaining a teenager outside a north London school, with the pair appearing to be involved in a struggle.
The officer can be seen swinging his arm towards the boy – but it does not connect, and they both end up on the floor.
Scotland Yard has referred itself to the police watchdog following the incident in Tottenham earlier this week.
In a statement about the footage, which was shared on social media, the Metropolitan Police said officers stopped a group of males in West Green Road at around 4.50pm on Tuesday, detaining one of them for a search.
“A crowd formed and officers made a circle around the male," the force said in a statement.
Three officers were injured during the incident, and four teenage boys – all aged 16 – were arrested, according to the Met.
"It is important to remember that videos show a snapshot in time and the wider context is not immediately obvious," Detective Chief Superintendent Treena Fleming said.
Black Lives Matter Movement called for a protest marching to Tottenham police station on Friday afternoon following the incident, which they called a “violent assault on [a] child” in a tweet.
Gary McFarlane from Black Lives Matter Movement told The Independent the community was “shocked” by the video, and said the teenager in question was outside the school “to pick up certificates”.
A Met spokesperson told The Independent: “We are aware of a protest taking place outside Tottenham Police Station and an appropriate policing plan is in place. “
In a statement over the video, Det Ch Supt Fleming, said: "I am aware of videos circulating on social media showing part of the incident and we are working to establish the full circumstances of what occurred.
"A criminal investigation is under way to ascertain how the officers received their injuries and welfare support is being provided to them.
She said: “A public complaint has been received and we recognise the community concern around this incident so we have made a voluntary referral to the Independent Office for Police Conduct. The IOPC has taken the investigation as independent.”
Det Ch Supt Fleming added: "I would ask that our communities allow us the time for the incident to be reviewed in full so that all the circumstances can be established."
The Met said the four teenagers who were arrested following the incident have been bailed to return to a north London police station in January.
Additional reporting by PA