Mid and West Wales Fire Service said there were two casualties and two further "walking wounded" involved in the incident on Fabian Way in Swansea.
Police, firefighters and paramedics were called to the incident.
A British School of Motoring (BSM) spokesperson said they were looking into the incident involving their car.
Two people in a learner driver's car had to be rescued by firefighters after it flipped on to its roof following a collision with another vehicle.