Police say arrests were made and fines issued after crowds of fans gathered to celebrate Rangers winning the Scottish Premiership.
Large numbers of supporters made their way to Ibrox Stadium and Glasgow's George Square to mark the achievement despite warnings to stay at home.
Nicola Sturgeon said the crowds were "infuriating and disgraceful" and could delay the end of the Covid lockdown.
The result gave Rangers an unassailable 20-point lead and the title for the first time in 10 years.
Under current guidance, public gatherings are banned and a maximum of two people from two households are allowed to meet outdoors.
Football games are taking place behind closed doors with no fans in the stadium.
However, following Sunday's game, crowds of fans took to the streets, as some let off flares while others chanted and waved flags outside the club ground. In Glasgow city centre fans flocked to George Square to celebrate being crowned Scottish champions.
In a tweet, First Minister Nicola Sturgeon congratulated Rangers on the title win, but added: "Gathering in crowds just now risks lives, and could delay exit from lockdown for everyone else."
"If those gathering care at all about the safety of others & the country, they will go home," she said.
In a later tweet she said: "I share folks' anger at this."
She added it was "infuriating and disgraceful" to see the crowds "risk our progress" after everyone complying with lockdown rules has made "so many sacrifices".
I congratulate @RangersFC on the title win & recognise what a moment this is for fans. But gathering in crowds just now risks lives, and could delay exit from lockdown for everyone else. If those gathering care at all about the safety of others & the country, they will go home. https://t.co/MjzJJEhhsd— Nicola Sturgeon (@NicolaSturgeon) March 7, 2021
I share folks’ anger at this. Everyone has made so many sacrifices in the past year & seeing a minority risk our progress is infuriating & 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 https://t.co/haH5DAzhIh— Nicola Sturgeon (@NicolaSturgeon) March 7, 2021
Ch Supt Mark Sutherland said officers attended gatherings at both George Square and outside Ibrox stadium.
Arrests were made and fixed penalty notices issued for breaches of the Covid restrictions, disorder incidents and the use of pyrotechnic devices, he added.
In a statement published shortly before 21:00, he urged fans to make their way home.
The PA news agency reported that by 21:30 police officers had encircled a depleting group of fans at the base of the Scott Monument in George Square.
Last May thousands of Liverpool fans flouted social distancing guidelines and gathered outside Anfield to celebrate the club's first Premier league title in 30 years.
And in November hundreds of Celtic supporters defied the level four restrictions and converged on Celtic Park to call for the removal of the club's then manager Neil Lennon.
David Hamilton, chairman of the Scottish Police Federation, said he was "appalled" by the scenes.
He also told the BBC Radio's Good Morning Scotland programme that officers, many of whom have not been vaccinated, were put in "jeopardy" by the supporters' actions.
Mr Hamilton said he understood why people were frustrated by the Police Scotland response but said that was an operational matter for the force, which would have considered factors such as wider public order issues and road safety.
He highlighted that it can take up to 20 minutes to issue a fixed penalty fine for breaches of the Covid restrictions.
Mr Hamilton said: "If we were to ticket everybody in George Square yesterday we would still be doing it just now."
But he also criticised the club for being "silent" and failing to address the mass gatherings on its social media accounts.
He added: "There is a responsibility to the club here. It should not take the government to have to ask the club to tell people to go home.
"That should have been something the club should have taken on themselves proactively."
The club tweeted or retweeted more than 50 times in the hours after they were crowned champions but did not address the mass gathering of fans.
Social psychology expert Prof Stephen Reicher said the celebrations were "completely predictable" and "in some ways encouraged".
The St Andrews University academic said it was "disappointing that the club did not have a dialogue with the fans about how one can celebrate but in ways that are safe, in ways that don't endanger the public, that don't endanger and, indeed, don't endanger Scottish football".
He warned that it undermined the argument for safely reopening mass events including the Euros championship in Scotland.
Glasgow Kelvin MSP Sandra White described the celebrations as "absolute chaos" and questioned what plans were in place to prevent mass gatherings.
She told Good Morning Scotland: "They [the fans] should never have been allowed to leave Ibrox and march into the city centre in large numbers. It could have been stopped there and then.
"People have lost loved ones and people can't visit loved ones and yet this is being facilitated."
Rangers fans in Northern Ireland also breached lockdown rules, with a large crowd gathering on Belfast's Shankill Road to celebrate on Sunday evening.
Police Service Northern Ireland urged people to celebrate "at home safely and within the current health regulations".
Earlier on Sunday Scotland's justice secretary urged fans not to put lives at risk by flouting lockdown rules.
Humza Yousaf also warned that Uefa would be paying "close attention" in anticipation of the European Championships coming to Scotland.
Following their win, some Rangers players made their way to the fence to celebrate in sight of fans outside.
Speaking on BBC Scotland's Sunday Show, Scottish Conservative leader Douglas Ross called the actions of fans outside Ibrox "completely wrong".
He added: "We've all done so much to get the virus rates down.
"I understand passions run high with football fans, but it clearly didn't match what we expect people to do during a Covid period, while many people still can't even leave their homes."