The incident is on Barnsley Road, outside Longley Park Sixth Form.
It is not yet known if anybody in the car was injured.
The incident is expected to cause issues in the local area as children make their way to the sixth form centre this morning.
Bus company First South Yorkshire said: “Due to an incident on Barnsley Road (outside Longley College), service 18 will be diverted via Crowder Rd and Elm Lane in both directions.
“Service 32 and 32a will be diverted via Hucklow Road and Stubbin Lane in both directions.