It happened at around 7:30 Tuesday morning at Clinton and Fruit.
The California Highway Patrol says a sedan collided with a pickup truck in the intersection.
The truck then hit a signal light pole, while the sedan was pushed into the school bus that was stopped at a red light.
A Fresno Unified spokesperson says 12 students were on board at the time, but none of them were hurt.
Two were taken to the hospital as a precaution at their parents' request because they are non-verbal.
A tire from the pickup flew into two other stopped cars.
One of those drivers went to the hospital with a complaint of pain, and the passenger in the sedan went to CRMC with minor injuries.
It's unclear right now which driver ran the red light.