It happened around 6:30 a.m. Wednesday near the intersection of 34th Street and Grays Ferry Avenue.
Surveillance video shows a black car making an illegal left turn out of the Conoco gas station at the intersection moments before the crash.
There is a raised median in the middle of Grays Ferry Avenue, so the driver went down the wrong side of the road toward traffic to get around it.
Surveillance: Truck crashes into back of school bus in Philly
The car left the frame of the camera, but moments later the school bus is seen slamming on its brakes.
A city employee on the scene told Action News the car swerved in front of the bus and kept going.
The Streets Department crew was in a small dump truck behind the bus. The small truck, with a flat front, is used on narrow city streets.
When the bus driver hit the brakes, the dump truck crashed into the back of the bus.
The two workers were transported to the hospital with unknown injuries.
The accident blocked a lane and slowed traffic for at least three hours in this busy area during the morning rush.
Officials with the School District of Philadelphia said four students were on the bus heading to Furness High School.
The students were taken the rest of the way on another bus.
There were no reported injuries to anyone on the bus, according to school district officials.
Police are searching for the driver of the wrong-way vehicle.