Mr Kerr described scenes of Rangers’ fans fighting and lashing out at police officers as “unacceptable” and “violent thuggery”.
His response came after confirmation that at least five officers had been injured and 20 arrests had been made made in Glasgow as Rangers’ supporters refused to disperse from George Square on Saturday.
”My message is clear that if you have been involved in these ugly scenes, then we you will be identified and arrested," said Chief Constable Mark Sutherland in his statement on Sunday morning.
Footage circulating on social media over the weekend showed celebrations becoming violent as some fans turned on each other and police officers at the scene.
One video, tweeted by Merchant City PubWatch chairman Gerard Febers, was taken from inside Italian restaurant La Vita on the corner of George Square.
The footage showed a crying young woman being pushed up against the window while fans in the background threw barriers at police officers in riot gear forcing them out of the square.
Mr Febers had also tweeted late on Saturday night to voice concern for staff safety and welfare, saying “30 years as a publican and I’ve never felt so vulnerable or intimidated as I did today”.
He said he had closed his establishment early, “not because of the abuse directed at me from 9.45am this morning, but to protect my staff who started their shift at 6pm who also were subjected to abuse”.
A Cafe Andaluz branch on St Vincent Place was also forced to close early on Saturday night as violent scenes took place outside the restaurant.
Late night footage also captured the mess left behind, with empty cans, plastic bags and glass bottles strewn across George Square.
Following a clean-up operation by Glasgow City Council staff on Sunday morning, the local authority issued a statement on social media ahead of further scheduled protests in George Square on Sunday, saying:“If you are thinking of gathering in George Square or anywhere else in the city, please don’t.
"Cases in Glasgow are rising again. Staying safe, sticking to the rules will help us all fight the virus ‘til it's done.”