It happened on North Main Street and East 36th Street around 7:10 p.m.
The officer stopped a vehicle for illegal equipment and window tint when the driver tried to take off, according to Houston police. That's when the officer was dragged while holding on to the door of the car, police said.
Both the officer and the driver ended up on the ground after the car crashed into a fence and shots were fired during a struggle, hitting the driver in the leg and arm, according to HPD Assistant Chief Shondra Hatcher.
"The suspect turned the steering wheel all the way to the right, and attempted to flee the scene in a high rate of speed," Hatcher said.
Both were taken to a hospital where they were stable.
The officer may have a concussion from hitting his head, according to Hatcher.
Neither the officer nor the suspect were immediately identified.
HPD's homicide and internal affairs units were investigating along with the Harris County District Attorney's Office.