Officers in Scotland say many more arrests will follow after a section of Rangers supporters shouted anti-Catholic slogans and songs along with damaging property in Glasgow.
Scotland's First Minister and Deputy First Minister have spoken out against the scenes on Saturday which led to five police officers being injured and 30 arrests.
Thousands of fans defied Covid-19 warnings against large gatherings and massed in George Square to celebrate Rangers winning their first Scottish Premiership championship since 2011.
Images showed George Square strewn with hundreds of broken bottles, plastic bags and spent flares after flag-draped fans had been seen attacking each other and launching traffic cones, plastic bollards and other missiles at lines of riot gear-clad police officers.
On Twitter, Nicola Sturgeon described the scenes as disgraceful. She added she was "angry on behalf of every law abiding citizen."
"In normal times, the violence and vandalism, and the vile anti Catholic prejudice that was on display would have been utterly unacceptable. But mid-pandemic, in a city with cases on the rise, it was also selfish beyond belief," she said.
John Swinney, deputy first minister, told the BBC's Good Morning Scotland: "Every exhortation was given by Police Scotland, the Scottish Government and Rangers Football Club for fans not to assemble.
"But unfortunately 15,000 people did so and they started off behaving peacefully and then they descended into thuggish behaviour in George Square.
"I'm limited as to what I can say this morning because there's an ongoing police investigation but the conduct on Saturday was absolutely reprehensible.
"There was absolutely no need for them to gather, absolutely no need whatsoever, and the warnings were given very clearly... and then some of them went on to behave in a loutish and thuggish fashion in George Square - devastating property, circulating and expressing vile anti-Catholic bigotry in the centre of the city of Glasgow.
"Police officers were assaulted on Saturday, which is completely unacceptable and obviously that will be a matter which is pursued vigorously by Police Scotland and so it should be and there'll be various actions taken to address the behaviour and the conduct of the fans on Saturday."
Calum Steele, general secretary of the Scottish Police Federation (SPF), tweeted images on Sunday night of some of the injuries sustained by officers, including broken bones and lost teeth.
A statement from Rangers said: "Winning our 55th league title in our 150th year was a historic day for Rangers Football Club. The support from millions of our fans across the world has been incredible.
"The achievement by Steven Gerrard and his team has received plaudits from across the football family, including recognition by sports writers, opposition players and managers.
"We are grateful to Scottish Government officials, Glasgow City Council and Police Scotland for the constructive engagement in the lead up to the weekend’s game. We worked closely with the authorities for two weeks before Saturday’s match to ensure a consistency of message.
"Sadly, a small minority of people behaved inappropriately and in a manner not reflective of our support. Some of the scenes were unacceptable and have besmirched the good name of Rangers Football Club. These so called "fans" should reflect upon the values and ethos of our club, and consider the damage this does to the reputation of the club.
"We will continue to engage with authorities as required."