Montreal police said the incident started sometime before 2:30 a.m. near the intersection of St-Catherine and St-Hubert.
"The hypothesis that investigators are looking at now is that there was a conflict between two men and it tuned into a knife fight and they were injured in the fight," said Const. Simon Delorme.
Police were called to the scene after receiving a report about a man with injuries to his lower body. That man, who is in his 20s, was taken to hospital for treatment of cuts to his leg.
While police were on the scene, they located a 27-year-old man in the park with wounds to his upper body. His condition was initially considered life-threatening, but he later stabilized.
Police say neither of the men involved is cooperating with investigators.