Police say the officer pulled the driver over at a checkpoint near Third Avenue and 111th Street just before 5:30 p.m. and discovered he had a suspended license.
When the officer went to arrest him, they say the driver took off, dragging him a few feet.
The officer was taken to the hospital with minor injuries to his leg.
Investigators say the driver is a 23-year-old man in a 2004 Mercedes Benz.
Anyone with information on the case should contact the Crime Stoppers hotline at 1-800-577-TIPS, or text CRIMES and then enter TIP577, or visit www.nypdcrimestoppers.com.