Rangers boss Steven Gerrard has condemned the violence that occurred outside Ibrox before his side’s Europa League clash with Osijek.
The pair, aged 24 and 40, were injured when a “large-scale disturbance” involving up to 40 people broke out in the Govan area of the city on Thursday evening.
The victims, both now revealed to be Croatian nationals, were taken by ambulance to Glasgow’s Queen Elizabeth University Hospital for treatment.
Police Scotland said the younger man was released from hospital on Friday morning, while the 40-year-old was being discharged later in the day.
It is thought around 40 people were involved and detectives have described the incident as “disgraceful”.
Gerrard also criticised those taking part in the incident, saying: “As a club we don’t condone that type of behaviour, we don’t want to see scenes like that.
“We want everyone to come away talking about the football and the positive result we got.
“So it’s a shame that has gone on and we just hope that no-one has been hurt, that’s all we ask for.”
Officers were called to the scene at Edmiston Drive near Paisley Road West, a short distance from Ibrox, just after 7pm - shortly before the match which ended in a 1-1 draw, with Rangers progressing to face Maribor of Slovenia after a 2-1 aggregate win.
Footage on social media appeared to show fights between rival fans, with one clip uploaded to Twitter featuring scenes showing a supporter being kicked about the body while lying prone in the road, while another was seen running around holding a flare.
Police officers, including those on horseback, could be seen lining roads on the approach to the stadium.
Officers are appealing for information about the disturbance.
A dedicated team of officers is examining CCTV footage and carrying out door-to-door inquiries in the area to establish the full circumstances surrounding the incident, the force said.
Area commander Chief Inspector Alan Bowater said: “Supporters of both sides should be able to attend a football match without getting caught up in violence and disorder.
“Also, innocent members of the public should not have to be faced with the threat of encountering it.
“The individuals involved must be tracked down and held to account and Police Scotland will use every resource at its disposal to put a stop to this reckless behaviour.
“I would like to reassure members of the public that we take their safety extremely seriously and sufficient resources will be deployed at future games to tackle anti-social behaviour and violence.”
Detective Chief Inspector Craig Willison, of Greater Glasgow CID, added: “Extensive inquiries are ongoing to identify the individuals involved in this disgraceful incident. I would appeal to anyone who was in the area at the time, particularly those with mobile phone or dash-cam footage, to get in touch.”