Josiah Taylor was discovered unconscious and unresponsive inside the home on Mosel Avenue just before 1:00 p.m.
He was rushed to Staten Island University Hospital North, where he was pronounced dead.
The medical examiner's office has ruled the death a homicide. The boy suffered from battered child syndrome. He had injuries in various stages of healing, which the medical examiner said took place over a period of time.
Detectives are questioning the boy's mother and father. No charges have been filed yet against his parents.
The 18-year-old mother told detectives that the boy was already unresponsive when she shook him. She then made statements that may implicate the father, police said.