Police have launched an investigation to identify Celtic fans involved in violence following their team's 2-0 League Cup defeat by Ross County.
Ch Supt Mark Sutherland criticised "disgraceful" scenes that left three officers with minor injuries.
The disorder developed after hundreds of fans converged on Celtic Park to call for the removal of Neil Lennon.
Players and management had to be escorted from the ground while being targeted by missiles.
Police Scotland deployed officers, at least 12 vehicles and the force helicopter.
Glasgow is currently under level four of the Scottish government Covid restrictions, meaning protests are prohibited - however no arrests were made.
Ch Supt Sutherland said fans posed a "real risk of coronavirus infection" to officers and the wider community.
"My message is clear, if you are identified as being involved, you will be arrested. Don't think just because you weren't arrested last night that you have escaped justice," he said.
A large number of fans began to protest outside the Glasgow football ground at about 16:30, shortly after the match ended.
Violence 'aimed at police'
Supt Stevie Dolan said the police response was "appropriate" and the group later dispersed.
Justice Secretary Humza Yousaf described the scenes as "utterly disgraceful" and said violence was aimed at police during the protest.
"Officers have been front and centre keeping us safe during this pandemic, to treat them this way at any time is shameful," he said.
"To do it during these times is a disgrace."
The scenes came after Ross County ended a run of 35 cup wins for Celtic who had won the last 11 domestic trophies.
Celtic have now won just two of their last 10 matches. They also trail Rangers by 11 points in the league.
In a statement, Celtic vowed to investigate the disorder and condemned the violent scenes as "unacceptable".
It said it shared the "huge disappointment" of Celtic supporters but "there can be no excuse for some of the violent scenes at Celtic Park this evening".
"The club will be investigating these events fully," it added.
"For players and a management team, who have given so much in recent years and have delivered 11 consecutive trophies, to require an escort from Celtic Park while being targeted with missiles, is simply unacceptable.
"While we understand that only a small number of people were involved in this behaviour, some of the actions this evening, which have obviously left our own players shaken, cannot be condoned in any way."