It was reported to officers at about 10.10am on Sunday that a man had walked into the church on St Patrick’s Avenue and hit the priest, Fr John Murray, on his head with a bottle before leaving.
The victim was taken to hospital for treatment of a head injury, where he remains in a serious condition.
Detective Chief Inspector McBurney said: "This was a completely shocking and brutal attack and has left the priest with a serious head injury.
"Our enquiries are ongoing into this incident".