The crash happened at Tulare and M streets in downtown Fresno Wednesday morning.
Investigators say a car with a driver and passenger was going in the wrong direction and went through a red light, hitting the Fresno Unified vehicle.
M Street is a one-way street.
The driver, who was the only person in the district SUV, was taken to the hospital.
A second person from the other car was also hospitalized.
Their conditions are unknown at this time.