The altercation took place around 4 a.m. inside a McDonald's restaurant on the corner of Villeray Street and Saint-Michel Boulevard.
"[There are] many witnesses to meet with, and also in this case investigators will try to understand a little more about this conflict that degenerated between these three men," said Anie Lemieux, spokeswoman for the Montreal police.
The suspect, also in his early 20s, fled the restaurant before police arrived.
Police were also called to the scene of a shooting at around midnight near the intersection of Fleury Street and J. J. Gagnier Street in the Ahuntsic-Cartierville borough.
According to authorities, a man in his 50s was inside a parked tow-truck when he was hit by at least one bullet.
The victim attempted to drive off but hit three parked cars while driving in reverse.
"He stayed in his tow-truck and backed up on Fleury Street going east and hit three parked cars along the way and stopped in a parking lot" said Lemieux. "When police officers got there, they located the victim and he was taken to hospital quickly."
The man, who is known to police, sustained serious injuries but authorities do not fear for his life.Police are seeking a suspect in that incident as well.