Julio Acevedo, 44, was charged Thursday night with three counts of criminally negligent homicide, as well as leaving the scene, excessive speed, assault and reckless driving, The New York Times reported.
Acevedo, who was extradited from Pennsylvania where he turned himself in to authorities, could face 15 years to life in prison if convicted.
The baby was delivered three months prematurely immediately after the late Sunday accident and died a day later, the Times said.
A spokeswoman for the chief medical examiner told the Times Thursday the baby died from "extreme prematurity" and because of "blunt force injuries" sustained in the accident.
Witnesses said they saw Acevedo speed around a fire truck and crash into the taxi carrying Raizy and Nathan Glauber, both 21, and then leave the scene. Acevedo allegedly said he was fleeing someone who had shot at him.
Cab driver Pedro Nunez Delacruz said he has no recollection of the crash.