The disturbance happened on the M74 northbound between junctions 2 and 1A at around 3.20pm on Sunday November 21.
It comes after footage emerged online of fights on coaches on the way to Hampden Park.
Hibernian and Rangers went head-to-head at the ground in the semi-final of the Scottish League Cup on Sunday night with Hibernian winning 3-1 against the Glasgow-based team.
Police Scotland has commented that they are aware of the videos circulating online as they are looking into the disorder on the motorway.
Police are asking anyone who was on the buses or anyone driving on the carriageway at the time to get in touch.
Detective Sergeant Darren Munogee at Cambuslang Police Station said: “Our enquiries are at a very early stage into the disorder on the motorway and we are working to establish more information on the circumstances and identify those involved.
“We are aware of the videos circulating online and we are urging anyone who was on the buses, or anyone driving on the carriageway at the time to contact us. We would like to hear from anyone who has footage of the disturbance as this will assist our investigation into this incident.”
Anyone with information should contact officers through 101 quoting reference number 2242 of 21 November. Alternatively Crimestoppers can be contacted on 0800 555 111, where anonymity can be maintained.