Sanitation worker Lou Pepe, 53, said he bought the display for the Sacred Heart of Jesus and Mary-St. Stephen Catholic Church.
New York Post said the Mary and Joseph figures were bolted down, but the Jesus figure was not.
The scene is worth $1,700, New York Post reported, and Pepe dedicated it to his late parents, Vincent and Vincenza Pepe.
The NYPD Hate Crimes Task Force said they are investigating the theft of the figure, worth $150.
"I am praying to St. Anthony of lost things and missing people that the baby Jesus is returned by [today], before we take the display down," Pepe said. "I am very upset. We want to reunite the family."
Wisconsin business offering 'therapeutic cuddling' forced to close
Campus cop fatally shoots Texas student during traffic stop