A 60-year-old custodian found the infant wrapped in towels inside a manger at Holy Child Jesus Church in the borough of Queens after returning from his lunch break on Monday.
The boy was in good health and transferred by paramedics to a hospital, police and church officials said.
Parish vicar Christopher Heanue said the baby weighed five pounds, two ounces (2.3 kilos) and measured 17 inches (43 centimeters).
"No one else was outside the church at the time -- 1:10 pm he returns from lunch and immediately hears a baby crying. He observes a newborn baby wrapped in towels, the umbilical cord still attached and lying in the nativity scene manger."
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Surveillance video footage reportedly showed a woman carrying the baby into the church and then leaving, just days before America celebrates its Thanksgiving holiday.
New York State law allows a parent to abandon a newborn baby during the first 30 days of its life -- anonymously and without fear of prosecution -- if the baby is left in a safe manner.
A hospital, staffed police or fire station are listed as suitable locations. Police said they were investigating.
"Let us pray for this child, for his parents and for whomever will receive him into their home," the vicar wrote on Facebook.
Officials are not yet sure of the mother's identity and the child is being cared for at a hospital.