The two-vehicle collision happened on the A5 south of Oswestry, at the Queens Head junction, at 1.40pm on Tuesday.
Firefighters from Oswestry extinguished the fire and then made the vehicles safe.
West Midlands Ambulance said the driver and passenger of the car that caught fire had managed to get themselves out of the vehicle before the arrival of the emergency services.
"Both sustained injuries and were given treatment on scene by ambulance staff and paramedics before being conveyed to Royal Shrewsbury hospital for further precautionary checks," a spokesman said.
Police closed the A5 for some time.
Emergency services were also called to a two-car road accident at 11.40am at Woolstaston near Church Stretton.
Ambulance staff assessed one woman, the driver of one vehicle, who sustained minor injuries but didn’t require hospital treatment and was discharged on scene. Firefighters make the vehicles safe.