Video shows a tall man in a dark jacket and white baseball cap rounding the altar and charging at Grou as he thrusts his right arm toward the priest.
No details were available on the identity of the suspect.
Father Grou was taken to the hospital in an ambulance.
"The suspect was then taken into custody, transported to a detention center and will be interviewed by investigators", she added.
The incident began shortly after 8:30 a.m. yesterday when a man with a knife rushed the sanctuary of the landmark church and stabbed 77-year-old Grou, the Oratory's rector. The priest is seen falling to the ground, but quickly getting up and backing away as security officers apprehend the attacker.
The suspect's name was not released and he is expected to be charged Saturday at the earliest.
Messages of sympathy filled social media. "Father Claude Grou, Canadians are thinking of you and wishing you a swift recovery". His life is now out of danger, they added.
"A place of prayers, and a place of calm, and a place of peace - even if there are some moments like that", he said while being wheeled out of the Montreal General Hospital Friday evening.
The attack at St. Joseph's Oratory came during the same week that city officials announced that a crucifix that had been in place at Montreal's City Hall since 1937 will be permanently removed.
Christian Lépine, the archbishop of Montreal, posted a statement on the archdiocese website thanking police, paramedics and parishioners for their response.
St. Joseph's Oratory, the largest church in Canada, is in the culturally diverse Côte-des-Neiges neighborhood.