The incident happened at Amsterdam Avenue and West 97th Street around 8:15 a.m.
Police say the teen driver of the vehicle was fleeing cops who spotted him driving recklessly when he lost control, jumped the curb and crashed into a wall. He hit the victims head on as they were crossing the street.
The child, identified as 4-year-old Ariel Russo was rushed to St. Luke's Hospital, possibly by police officers, where she was pronounced dead.
The 55-year-old grandmother was rushed to the hospital in critical condition. She has since been upgraded to stable condition.
The 17-year-old driver, identified as Franklin Reyes, was taken into custody at the scene. Police say the suspect had been stopped by officers about 10 blocks south of where the crash occurred.
As officers approached his vehicle on foot, the suspect sped off, made a left at West 97th Street and Amsterdam Avenue, and crashed.
The suspect was in police custody at Mount Sinai Medical Center for observation. He is charged with manslaughter and vehicular manslaughter.
Reyes' lawyer, Martin Schmukler, says that he does not have a driver's license, only a learner's permit. On the phone, Schmukler said this was a kid who got panicked and didn't mean to harm anyone. He was driving his parents' SUV.
According to NY State Law, anyone with a learner's permit cannot drive unless accompanied by someone 21 or older with a valid license. Reyes was alone in the car.
Reyes appeared in court Wednesday but did not enter a plea. He is due back in court on Friday.