Footage on social media showed dozens of fans fighting shortly before the game at Ibrox Stadium, with some brutally kicking and beating each other.
The victims, men aged 24 and 40, were both taken to Queen Elizabeth University Hospital. The younger of the two has since been released, while the second victim will be released later today, according to reports.
Local police said those responsible must be “tracked down,” and have appealed to the public for help.
“Supporters of both sides should be able to attend a football match without getting caught up in violence and disorder,” Chief Inspector Alan Bowater said, according to the Guardian.
“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 behavior.
“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,” he added.