The disturbance happened on Paisley Road West, not far from Ibrox where Rangers were playing Tottenham Hotspur on Saturday afternoon.
One man was charged with alleged mobbing and rioting offences and police assault, while another three were charged in relation to alleged breach of the peace. offencesPolice officers have been attacked with street furniture as they dealt with the disturbance involving football fans.
One officer needed medical treatment following the incident.
Chief Superintendent Mark Sutherland, Greater Glasgow's Divisional Commander, said: "Around 1.30 pm on Saturday, 23 July, 2022, police officers were attacked with street furniture on Paisley Road West, near to Seaward Street, as they prevented a disturbance between rival football supporters."
He added: "There have been a significant number of football fans intent on causing disorder and violence across the city this afternoon and police officers have had to act swiftly and robustly to ensure public safety and reduce disorder."
Mr Sutherland said that as a result of this, he has authorised officers to use powers available under Section 60 of the Criminal Justice and Public order Act of 1994 - which allows officers to stop and search people where this is appropriate and necessary, either in vehicles or on foot.
He said: "This power, which is only authorised when absolutely necessary, also allows officers to require the removal of any item the officer believes is being used wholly or partly for the purposes of concealing their identity.
"As we approach the new football season I would make it clear that this behaviour will not be tolerated. It impacts other members of the public and the vast majority of football supporters who are in the city to enjoy the game."
A Police Scotland spokesperson later confirmed the four arrests, saying: "There were four men arrested in relation to the football disorder in Glasgow on Saturday, 23 July, 2022.
"A 24-year-old man was charged with alleged mobbing and rioting offences and police assault, whilst a further three men, aged 25, 27 and 51 years, were charged with alleged breach of the peace offences."
Tottenham Hotspur won Saturday's game 2-1.