Seven people were injured - four of them seriously - after a large group of men targeted pubs used by Celtic fans in the Gallowgate area at about 19:00.
Two of those hurt remain in a serious but stable condition in hospital.
Police said that the men responsible were dressed in black with hoods and scarves covering their faces.
Four men, aged 52, 37, 27 and 25, were taken to Glasgow Royal Infirmary following the disturbance and treated for serious face or head injuries.
Two of the men, aged 37 and 27, are still detained. The other two men were released after treatment.
Three other men suffered minor injuries but did not require medical treatment.
Det Insp Colin Hailstones said: "We are still at the early stages of this inquiry and would appeal to anyone who was in the area, who has mobile phone footage or any information that will help us with our inquiries to come forward to police.
"It would appear that this disturbance took place when a large group of men, described as being dressed in black with hoods and scarves covering their faces, tried to gain access to some of the pubs in the Gallowgate and started to challenge patrons within. This then developed and people spilled on to the street where the assaults took place.
"We have been checking CCTV in the area and have already spoken to people who were there at the time as part of the investigation for which there is a dedicated team off officers involved."
Several hundred Ajax fans were given a police escort to the stadium before the game which Celtic lost 2-1.
Police made four arrests in or around the stadium - one before, two during and one after the game - for alleged minor public order offences.
Meanwhile, an Ajax fan has been given a 12-month football banning order after pushing a police officer on the way to the the game at Celtic Park.
At Glasgow Sheriff Court, Jordy Van Mieghem, 23, from Amsterdam, admitted assaulting PC Robert Chalmers at London Road and also being in possession of cocaine.
Sheriff Ian Miller fined the mortgage advisor a total of Â£500 and banned him from any regulated UK game.
Ajax fans are thought to be responsible for a major disturbance in Glasgow on Thursday before their team's Europa League game against Celtic.