Deputy First Minister John Swinney said the "silence from Rangers was deafening" as he criticised the club for failing to order thousands of fans gathered in Glasgow on Sunday to go home.
Police made 28 arrests after fans congregated in George Square and outside Ibrox to celebrate Rangers' first Scottish Premiership title in 10 years.
Reasons for arrest included assaulting police officers, breaching coronavirus regulations, disorder, use of flares and sectarian breaches of the peace.
Speaking at the Scottish Government's coronavirus briefing on Monday, Mr Swinney congratulated the club on their win and praised those who celebrated at home but said the behaviour of some fans was an "absolute disgrace".
He said: "To see so many people deliberately flouting (coronavirus) rules with no regard for the safety of others is shameful.
"Events like yesterday risk spreading the virus and they show no regard or respect at all for the millions of households across Scotland who have been sticking to the rules, who haven't been able to meet up with friends and families to fully celebrate birthdays and other milestones or, in some cases, to attend funeral services of their loved ones.
"The Government and Police Scotland reminded Rangers of the need for the club to advise fans to adhere to the current restrictions in discussions on February 26 and March 5.
"It is a matter of profound regret that that did not happen.
"The Scottish Government will be making our extreme disappointment at the lack of leadership clear to the team management."
He said Rangers had a "duty" to tell fans not to gather and messages from them on Sunday could have helped disperse the crowds, adding: "The silence from Rangers was deafening."
Chief medical officer Gregor Smith told the briefing there is a "real risk" of a rise in Covid-19 infections following the gatherings.
Mr Swinney warned this could mean "difficult decisions" regarding lockdown easing.
In a statement, Rangers said: "During the last number of weeks, Rangers can confirm that we initiated open dialogue with key stakeholders in relation to the possibility of us achieving a historic 55th league title.
"We have proactively engaged with our local MP, the Justice Minister, the Scottish Government, Police Scotland and the SPFL in relation to maintaining a cohesive message regarding public safety during the Covid-19 pandemic."
The club said they understand the "jubilance" of their fans and highlighted "frustration" over the closure of stadiums.
The statement continued: "We reiterate the message from our manager, Steven Gerrard, who highlighted that fans should adhere to government guidelines: stay safe, socially distance and look after each other in this difficult time."
Club Statement: https://t.co/6uQBRrUUSP pic.twitter.com/d4nO7GwY1Y — Rangers Football Club (@RangersFC) March 8, 2021
The club said they will continue talks ahead of future milestones to "maintain a cohesive message in relation to government guidance".
Police Scotland 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."
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
He added there were a number of minor injuries to members of the public, some through intoxication.
He said the police operation was pre-planned and praised officers, saying many "put their own health at risk".
First Minister Nicola Sturgeon said on Sunday the "infuriating and disgraceful" scenes could jeopardise plans to ease the coronavirus restrictions and urged Rangers to ask people to go home.
