Two men were chased by a group of Coventry City fans as the club celebrated promotion, police have said.
West Midlands Police said a "good natured" gathering turned sour when a disturbance broke out.
Video shared online - believed to show the incident - shows two black men standing behind bins as a group throws bottles and other missiles.
The force said both men were searched, after it was alleged one had brandished a knife, and escorted from the scene.
The video shared online shows three police officers arrive and attempt to stand between the crowd and the two men.
More items are thrown and a window is broken, before one of the two men is put in handcuffs.
Hundreds of supporters had gathered in the city centre on Tuesday evening to mark the club's ascent to the Championship.
No-one was injured amid the skirmish at about 21:15 BST, the force said, but an "intoxicated" 17-year-old male was taken to hospital after falling and sustaining a head injury.
A window was broken during the disturbance, and a knife was later recovered from a bin, the force said.
Another video posted online, apparently filmed next to the Lady Godiva statue in Broadgate, where the celebration took place, shows Black Lives Matter placards on the ground.
A man's voice can be heard suggesting the signs be gathered up to "make a bonfire".
Many posts on social media using Black Lives Matter-related hashtags suggested there was a racial element to the incident.
West Midlands Police is calling for the public to help "establish the complete circumstances around what happened".
It said if any hate crimes are identified, it "will take action against offenders".
It said it would be investigating claims the two men were earlier armed with a knife and also claims that some of the crowd were in possession of weapons.
Coventry City FC said it was aware of the videos and would "liaise directly" with police.
The club said it was "clear and long-standing in our anti-racism and discrimination stance", and had supported Kick It Out - the campaign against racism in football - and the Black Lives Matter campaign".