Many trains had been cancelled ahead of the 15:30 kick-off with ScotRail warning of a driver shortage.
Large groups of fans could be seen walking through the city centre from about 13:00, escorted by police.
However violence soon erupted, with one group charging down Argyle Street towards the Trongate. Shoppers trying to leave can be seen screaming and running back indoors to avoid the rush.
One football fan falls to the group while others run around him shortly before a flare is set off near a shop doorway.
A shopper told News they were forced to take refuge in a nearby shop “for their own safety”.
An officer can then be seen using his baton on a number of fans passing by.
Police Scotland said officers had been authorised to use stop and search powers under Section 60 of the Criminal Justice and Public order Act 1994.
This allows officers to stop people when appropriate and necessary, either in vehicles or on foot.
Ch Supt Steve Dolan said: “Officers have had to act swiftly and robustly to ensure public safety and reduce disorder.
“The use of weapons or violence will not be tolerated and officers will take action where necessary to ensure safety.
“It impacts other members of the public and the vast majority of football supporters who want to enjoy the cup final event safely. Officers will remain in the city as our operation continues and anyone with any concerns can approach them.”
