Authorities said Christopher Norman Jost, 46, grabbed a 19-year-old woman as she was taking photos outside a church on Sainte-Catherine and Bishop Streets on Saturday around 3:30 p.m.
Police said the suspect had keys to the church and, once in the basement, forced the student to touch him sexually.
Canadian correctional officials are also seeking Jost on different warrants.
He is six feet two inches tall and weighs 220 pounds. Police said he has blue eyes, short dark blond hair and speaks French and English.
They say he frequents Montreal's downtown core and Chinatown.
The suspect walks with a limp and may be getting around with a cane or adapted transport.
He was last seen wearing a light-coloured winter jacket.
Police say Jost is "emotionally unstable" and could be aggressive.
Authorities are asking anyone with information about Jost to contact Info-Crime or 911.