Two men, both aged 18, were taken to hospital with serious facial injuries following a disturbance at the John Paul Academy football park, Arrochar Street at about 6.40pm on Friday.
Another two men, both aged 19, were also injured but did not require hospital treatment.
Officers are appealing to the public for more information.
Detective Constable Peter Lagan, of Maryhill Police Station, said: “Four people were injured during this incident, two of whom required hospital treatment, and our inquiries are ongoing to establish the full circumstances.
“There were a number of people around at the time and I would ask anyone who has yet not spoken to officers to get in touch.
“If you can help please contact Police Scotland on 101, quoting incident 3229 of Friday, 16 April, or make a call anonymously to the charity Crimestoppers on 0800 555 111.”