The row between a group of men began on Saturday's 2.36pm Glasgow Central to Drumchapel train and continued on to the station platform at the final destination.
A 34-year-old man was hit and fell on to the track, suffering a leg injury. He was taken to the Western General Hospital and released after treatment. An 18-year-old man he was travelling with was unhurt.
Transport police are trying to trace four men in connection with the incident, all in their late teens to early 20s and with short dark hair.
One was wearing a green parka jacket with a red top, jeans and white trainers. Another was wearing a black jacket with a grey top, jeans and dark shoes.
The third man was wearing a white jacket, denims and white trainers and carrying a yellow bag, while the fourth was wearing a black jacket with a green top, black trousers and white trainers, and was also carrying a black sports bag.
They all left the station in the direction of Garscadden Road, police said.
It is understood that the incident involved supporters returning from the Rangers v Dundee United Scottish Cup match at Ibrox.
British Transport Police Detective Constable Andrew Egan said: "It is my understanding that this incident may have been football-related. This sort of behaviour will not be tolerated and others travelling on trains should be able to do so without encountering it.
"Anyone who was on the train or at Drumchapel station, which was busy at the time, is asked to come forward with information which may assist our inquiries."