The Williamsburg church had its first statue stolen in 2012, its second in May and the third has now been broken.
On Sunday evening, a drunken man high-fived the statue of Jesus and tried to kiss it, removing it from the base.
Speaking to The New York Post, Fr Anthony Hernandez said: "It's too much of a temptation."
The administrator of the Saints Peter and Paul Church in Brooklyn said that he was "a little frustrated."
He added: "But I'm happy to see it doesn't seem to be a bias or hate crime.
"It just seems they were intoxicated."
The three-foot white statue was high-fived and kissed around 4:30am on Sunday, according to CCTV.
As the man pulls the statue towards him it snaps off the base and the group head off once they realise it has broken.
Fr Hernandez went on: "There's a number of clubs and bars down the road, so when they empty out, they pass by, and [the statue] is accessible. You can reach it from the sidewalk.
"I think I'm probably going to replace it, it's too much of a target.
"I was thinking of putting a large crucifix."
He joked: "It's the Year of Mercy but we'll put the next one out of reach."