Officials say it happened around 11 p.m. near Broad and West Norris streets.
Officers stopped a car in an attempt to help with a flat tire when one of them smelled marijuana and thought they saw a gun in the car.
Officers say the driver began to act suspicious and then drove off, dragging one officer and hitting a SEPTA police car with someone in it.
One of the officers shot the suspect in the arm.
The suspect tried to run away but was eventually caught and arrested by police.
The officer that was dragged and the SEPTA official that was in the car suffered minor injuries and are expected to be ok.