Montreal police were called to the corner of Jeanne-Mance Street and Van Horne Avenue just after 9 a.m.
They found a 37-year-old man in an alley with stab wounds to his upper body.
"We can now confirm that is a suspicious death. For now the investigators are still trying to identify elements to clarify the situation," said Éric Labad, spokesman for the Montreal police.
A 36-year-old woman near the scene, who had "family ties" to the victim was arrested and brought in for questioning.
Labad said the two were not husband and wife, but he would not specify how they were related.
A weapon has not yet been recovered.