Police say the man was driving along the 1800 block of Ellsworth Street when he hit two parked cars, then continued to the 1700 block where the woman was hit along with two more parked cars.
Investigators say the man fled the scene but returned a short time later.
The woman was hospitalized and is listed in critical condition after suffering a head injury.
A passenger in the suspect's car was questioned by police and released.
The suspect has not been identified at this time.