It happened just after 1 a.m. near Soundview and Seward Avenues in the Soundview neighborhood.
Investigators say the marked vehicle had its lights and sirens on as it was traveling eastbound on Seaview Avenue when it was struck by an incoming vehicle traveling northbound.
The police vehicle had been responding to a call for backup.
Four officers suffered minor injuries during the incident.
The 25-year-old driver of the other vehicle was taken to NYC Health + Hospitals/Jacobi Medical Center for back pain.