Shoppers could be seen screaming and running back indoors to avoid the rush.
Online footage showed one football fan fall to the ground while others ran around him. A short time later a flare was set off near a shop doorway.
An officer was then seen using his baton on a number of fans passing by.
A shopper told BBC News they were forced to take refuge in a nearby shop “for their own safety”.
CCTV footage from Gallagher’s Bar on Howard Street showed a masked man being punched in the face as he tried to enter the pub of Celtic supporters.
Moments later a flare was thrown through the doorway while fans charged along the street outside.
During the disorder, a Police Scotland officer was injured after missiles were thrown and a 26-year-old man was also taken to hospital after being seriously assaulted.
Officers were authorised to use stop and search powers, including removing items being used to conceal identity.
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