In a statement police say Robert Maraj was walking along a road in Long Island on Friday night when he was hit.
After the driver left the scene, the 64-year-old was taken to hospital where he was pronounced dead the next day.
Officers from Nassau County Police Department say "the investigation is ongoing", and the rapper hasn't said anything publicly yet.
The statement didn't say Robert Maraj was Nicki Minaj's dad, but a police spokesman confirmed to AFP that he was her father.
The rapper - whose real name is Onika Tanya Maraj-Petty - was born in Trinidad and Tobago and raised in the Queens borough of New York City.
She's been nominated for 10 Grammys, won five MTV Video Music Awards and broken the record for the most Billboard Hot 100 entries by a solo female artist.
She announced she was 'retiring' in 2019 but has released new music since then.
The 38-year-old recently paid $450,000 to the singer Tracy Chapman to settle a copyright dispute after sampling one of her songs.