Witness Adele Plamondon told public broadcaster Radio-Canada the priest - who escaped with minor injuries - was about to start reading the gospel, when "this man drew a knife and ran up to stab him".
Grou began moving away as the attacker knocked over a candle, CTV said, but video shows the man catching up to the priest, pushing him to the ground before appearing to stab him.
Montreal police say one individual has been placed under arrest and the priest is now in the hospital.
Church spokeswoman Celine Barbeau said Grou, the church's rector, "was conscious when he left".
There is nothing to suggest the attack was linked to any political, religious or extremist group, said Montreal police spokesperson Caroline Chevrefils.
Police have not yet released details as to the motives of the attacker.
Priest stabbed during Mass in Montreal
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. He is expected to appear by video feed Saturday afternoon at the Quebec Court Criminal Room.
"This was an isolated attack, and there is nothing to link it to terrorism", she added.
Church security guards ran to the rescue of the priest as the man stood holding the knife and very determined to kill the man of God.
Grou said he was thankful to all those who rushed to his aid and those who supported him.
Montreal's mayor, Valerie Plante, condemned the act of violence.
Encouraging people to pray and remain calm, Archbishop Lapine added, "Let us pray to St. Joseph and believe in peace". The Oratory gets about two million visitors a year, including pilgrims and tourists from around the world.
The incident happened on Friday in Montreal.
Previous Biden +8 Over Bernie In New Poll On 2020 Dem Field
In the first 24 hours after their announcements, O'Rourke hauled in $6.1 million and Sanders collected almost $6 million. The reports about a possible Biden-Abrams ticket raises new questions about Biden's meeting with Abrams last week.