Thousands of supporters defied Covid-19 warnings against large gatherings and massed in George Square in Glasgow to celebrate the club winning their first Scottish Premiership championship since 2011.
The square was strewn with hundreds of broken bottles, plastic bags and spent flares after flag-draped fans had been seen attacking each other and launching bollards and other missiles at riot police.
Five officers were injured and 28 arrests were made – with the force saying many more will follow.
Detective Inspector Craig Warren, who is leading the investigation, said: “The public can be confident we are doing everything possible to identify those responsible for the violence and disorder on Saturday.
“This will take time due to the numbers involved.
“Rest assured, if you were involved in causing this disorder, violence or anti-social behaviour you will be arrested.
“We are reviewing CCTV, video and still images and I would appeal to anyone who may have captured incidents on their mobiles to please get in touch with us. You may have footage that could help us in our investigation and it’s vital we speak with you.
“The Major Incident Public Portal (MIPP) is now available for the public to send any information, photographs or images directly to the investigation team.”
Deputy First Minister John Swinney told the BBC’s Good Morning Scotland: “There was absolutely no need for them [Rangers fans] 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.”
It comes as officers are also looking into social media footage of players appearing to use sectarian language during the celebrations.
A police statement said: “We are aware of a video circulating on social media apparently showing Rangers players using sectarian language while celebrating on Saturday.
“We are assessing its contents and will liaise with the Crown Office and Procurator Fiscal Service as part of our inquiries.”
In a statement the club said: “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.”
In a further statement, the club added: “It is evident that this video was shared with an adjoining narrative which attempts to discredit our players and the reputation of Rangers Football Club.
“It is deeply concerning that this video has been taken as genuine and has been shared widely including by some political representatives who should be mindful of their influence and legal processes.
“Our squad is richly diverse. Sectarianism is unacceptable and has no place in our club which is underlined by our Everyone Anyone campaign.
“We are confident that no criminality took place, we have sought legal advice and look forward to cooperating with Police Scotland.”