Antiq Hennis was being pushed in a stroller by his father, Anthony Hennis, at the time of the shooting, The New York Times reported Monday.
Police say the 22-year-old father was probably the intended target of the Sunday night incident, and that he may know who fired them.
Police Commissioner Ray Kelly said Hennis is not answering questions by investigators.
Hennis pleaded guilty last year to selling heroin and is on probation, court records indicate. He has a history of drug arrests.
Police said Monday they were investigation the possibility the shooting was in retaliation for a dispute that may have involved Hennis or one of his associates.
Kelly said police were still trying to identify the father's contacts.