The Fresno Police Department says it happened around 3 pm near S. Elm and E. Grove Avenues.
A witness told police they heard a crash, saw a woman on the ground and a white car leaving the area south on Elm.
Police are investigating the incident as a felony hit and run.
There is no suspect description at this time.
The woman was taken to Community Regional Medical Center in critical condition.
Anyone with information is asked to contact the Fresno Police Department.