The video shows a supporter walking back from Wolves' match against Arsenal last Thursday and a policeman tripping him up.
The video was posted on English Footy Bible's Instagram page and has had over 15,000 views.
A West Midlands Police spokesman said: "The force is aware of a section of footage which was taken following the recent Wolves v Arsenal fixture.
"It comes after we tried to engage with a small number of fans suspected of being involved in anti-social behaviour."
Confirming an internal investigation had been launched, the spokesman added: "Our Professional Standards Department (PSD) are aware of the footage and will be conducting a review to establish the full context.
The six-second video starts when the policeman walks behind the fan and trips him up. When the startled fan turns around to look at the officer, the policeman points at him.
Wolves fans can be heard laughing and cheering and saying "he's just kicked him for no reason".
A Wolves fan, who did not want to be named, contacted the Express & Star about the video.
He said: "This is disgusting, the fan could have fallen over and been run over by oncoming traffic.
"Football fans get the worst publicity ever but nobody deserves to be tripped up when they are just walking down the road after a game."
Commenting on the video on Instagram Ashton said: "Major kick that took him out the game."
Jack Croucher added: "He could’ve been killed."
The policeman involved is believed to be a well-known officer, who normally goes away with Aston Villa fans to ensure there are no violent incidents at matches.
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