Officers said the crash occurred around 10 p.m. on Thursday at the intersection of Jefferson Avenue and Brookhaven Drive.
The driver, identified as 45-year-old Francis Portillo, was initially asked to remain at the scene while police assisted the victim. Authorities say she drove away, leading officers to pursue her.
Police were able to stop Portillo shortly after and take her into custody.
The victim was transported to a hospital with severe injuries.
Portillo was booked into the Fresno County Jail on multiple charges, including felony DUI and hit-and-run.