Robert Maraj had been walking along a road in Long Island on Friday evening when he was hit by the car, before the vehicle continued on its journey, police have said.
The 64-year-old was taken to hospital, where he died on Saturday.
Police have asked for any witnesses to the fatal crash to come forward.
A representative for the US rapper confirmed the death to TMZ, although she has not made a public statement.
Minaj, whose real name is Onika Tanya Maraj, was born in Trinidad before being raised in the New York City borough of Queens.
The death of her father comes just four months after she welcomed her first child with husband Kenneth Petty.