In the video, the boy is punched in the stomach, chest and throat before he is handcuffed and dragged off the ground by the officer, then led to a police van.
Another teenager can be seen being pulled from the ground as he is arrested.
After a complaint was made on Saturday, the force said its professional standards team would look into the incident.
“While we look to establish the full circumstances of what happened, we would urge people not to speculate and avoid sharing rumours or misinformation,” the force said in a statement published on its website.
The incident happened the night before Halloween, on what in Liverpool has become known as “Mischief Night”.
“We are determined to protect our communities from the sort of appalling behaviour that we historically see at this time of year.
“We have a contempt for criminality and a commitment to cracking down on people committing serious offences in Merseyside,” a force spokesman added.