Emergency services were deployed to the smash on Lowedges Road, Lowedges, on Tuesday night.
The 19-year-old motorcyclist involved was taken to hospital with injuries that are not thought to be life threatening.
He was arrested on suspicion of assault, public order offences and riding a stolen motorbike.
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He remains in police custody.
Witnesses to the incident or anyone with information should call South Yorkshire Police on 101.