Officers were called to the intersection of Shields and Parkway at about 11 a.m. Tuesday morning.
Witnesses say the driver hit one wheelchair with his car, knocking the victims into each other and out of their chairs.
A person who saw the accident followed the driver, caught up with him a few blocks away, then called police and detained the hit and-run suspect until officers arrived to arrest him.
Investigators say the driver will be charged with felony hit and run.
