Police said the AA Driving School Ford Fiesta was one of five cars involved in an accident near the ITV studios on Kirkstall Road near Leeds city centre at around 2pm.
The Fiesta driver, a man aged in his sixties, was taken to hospital for treatment after suffering a suspected broken wrist.
Police said a woman suffered neck and a back injuries and a second man suffered cuts during the collision, which also involved a Nisan Juke, Citroen Xsara, Audi A1 and a Hyundai i40.
Kirkstall Road was closed for more than an hour while police dealt with the incident.
Photos: Malik Walton