In St-Henri, a 26-year-old man was found injured on Walnut Street near Cazelais Street around 1:20 a.m.
Sgt. Daniel Lacoursière said the man is in critical condition and is known to police.
"A passerby saw a man lying in the street. He seemed injured, so police were called to the scene," Lacoursière said.
"The man was transported to the hospital where it was determined that he was wounded by a sharp object. So presently, the investigators are trying to determine what happened in this event."
So far, there are no witnesses or suspects.
In a separate incident downtown, a man was stabbed during a conflict on Ste-Catherine Street.
It happened at 3:20 a.m., just after bars closed down.
Police say the altercation began at the corner of Crescent Street, then moved to the corner of De la Montagne.
Lacoursière said the victim is in critical but stable condition.
A 24-year-old man and an 18-year-old woman have been arrested and are being questioned by police.