A further seven people were issued with fixed penalty notices or will be reported to the Procurator Fiscal.
Fans packed into George Square and gathered outside Ibrox Stadium after Rangers took their first top-flight title in 10 years.
Police said action was taken for offences including assaulting police officers, breaching coronavirus regulations, disorder, use of flares and sectarian breaches of the peace.
First Minister Nicola Sturgeon said the “infuriating and disgraceful” scenes could jeopardise plans to ease the coronavirus restrictions and urged Rangers to ask people to go home.
Chief Superintendent Mark Sutherland, divisional commander for Greater Glasgow, said: “Despite the coronavirus regulations and the prohibition of gatherings, our officers were faced with a very difficult set of circumstances as many thousands of supporters gathered to celebrate across a number of different venues.
“Our priority was public safety and this included reducing the risk of disorder, road safety and effective crowd management among the complexities of a vociferous crowd. This included established crowd control measures to prevent serious disorder in multiple areas and protect the public.
“An appropriate policing response was in place throughout the day and officers continually engaged and encouraged compliance with coronavirus regulations.
“Over the course of the day a number of minor injuries were sustained by members of the public, some of which were as a result of intoxication.”
He added: “Where it was appropriate to do so officers moved to enforcement for a variety of offences including breaches of coronavirus regulations, acts of disorder, pyrotechnic use and a number of arrests for assaulting police officers and sectarian-related breach of the peace.
“In total, 28 people were arrested and seven people were issued with fixed penalty notices or will be the subject of a report to the Procurator Fiscal.
“I am grateful to our officers who showed great commitment and professionalism throughout the course of the day, many of whom put their own health at risk during a challenging set of circumstances.”
He said the police operation was pre-planned.
Some politicians had criticised the police response, with Scottish Green MSP Ross Greer tweeting: “Expect Police Scotland to explain pretty quickly to Parliament why they decided to facilitate rather than disperse multiple mass gatherings during a national lockdown today.”
The SNP’s Sandra White posted on Twitter: “I’ll ask once again Chief Constable Livingstone what are Police doing? My constituents should not have to put up with this behaviour.”
Ms Sturgeon tweeted: “I share folks’ anger at this.
“Everyone has made so many sacrifices in the past year and seeing a minority risk our progress is infuriating and disgraceful.
“It is deeply unfair to the entire country, and the police have a hard enough job already.
“Please ask fans to go home @RangersFC”.
Justice Secretary Humza Yousaf also asked fans to stay at home, saying he understood they would be “desperate” to celebrate but must adhere to lockdown rules.
He warned Uefa would be paying “close attention” as Glasgow’s Hampden Park is due to host some games of the delayed 2020 European Championships in the summer.