A 39-year-old man is in custody after a 23-year-old woman was stabbed in Montreal's Milton-Parc neighbourhood near McGill University Thursday afternoon. She's recovering from an injury that police say doesn't pose a risk to her life.

The incident occurred outside at around 5:30 p.m. when authorities received multiple 911 calls about a person who was possibly stabbed at the corner of rues Milton and Durocher, SPVM spokesperson Véronique Comtois told MTL Blog.

Officers arrived to find the victim conscious with "at least one" wound to her upper body. She was brought to the hospital.

Police say the 39-year-old suspect fled the scene but was later found in a nearby residence. He was brought to a detention centre and was set to meet with investigators, Comtois said.

Officers had established a crime scene where the incident took place but have since left.

The investigation is ongoing.