Witnesses said there were around 15 people involved in the fighting close to Blackfriars Street.
It follows Celtic’s 2-1 victory over Rangers in a typically stormy clash at Parkhead.
One onlooker claims to have seen a Celtic fan “in a bad way after being stabbed”.
Police taped off Albion Street, in the Merchant City area, following the incident around 5pm on Sunday.
A spokesman for Police Scotland said: “Three men have been taken to hospital for treatment.”
A stabbing took place in the Strathduie pub on Blackfriars Street before the fighting carried on into Albion Street, it has been reported.
A witness claimed: “Three stabbed from what I heard. Saw one stabbed in shoulder and cut on forehead.
“Folk saying someone, young Celtic fan, in a bad way.”
Another onlooker said they saw fans get knifed in the neck and back.
They said: “Albion Street next to Italian Kitchen was where the guy was with a stab wound to the neck.
“Then on Blackfriars Street there were two others who were stabbed in the back.
“Looks like Celtic and Rangers fans met where Albion Street and Blackfriars Street meet.”
Another witness claimed there was mayhem.
They said: “It looked like utter chaos.
“I have never seen so many police in my life.
“The whole of the Merchant City seemed to be cordoned off.
“We came into town for a drink in the evening thinking the football crowds would be long gone but it looks like the trouble is just starting.”