A caretaker at a Queens church found the child wrapped in towels in the manger after returning from lunch on Monday afternoon.
Police say the baby is in good health despite being left in the Holy Child of Jesus Church in Richmond Hill for several hours.
They haven't confirmed the gender, and are searching for the person who left the child at the church.
State law says a new-born can be dropped off at a church, hospital, police or fire station, but it requires the child to be left with someone or for the authorities to be called immediately.
Police said that did not happen in this case, which has led investigators to begin searching for the person who dropped the child at the church.
Witnesses are being sought in a bid to track down the baby's mother.
Church pastor Christopher Heanue wrote on the church's Facebook page that the baby was a boy and weighed a little more than 5lb.
He wrote: "At midday today an abandoned new-born baby was found in a recently constructed manger scene in our church.
"With umbilical cord still attached, and wrapped in a blanket, the baby was found placed in the manger.
"Police was called and the baby was taken by ambulance to Jamaica Hospital where it is being treated.
"He is a healthy 5lb2oz boy - 17inches in length.
"Let us pray for this child, for his parents and for whomever will receive him into their home."