The incident took place on the B4555 just outside the village of Eardington, which is to the south east of Bridgnorth.
The saloon car left the road and ended up on its side about 20 yards down the embankment at just before 8.30pm last night.
Firefighters from Shropshire Fire and Rescue were called to the scene to help release the two people from the vehicle.
A West Midlands Ambulance Service spokesman said: “One of the occupants, a 42 year old woman was complaining of shoulder and foot pain while the 35 year old man had left sided chest pain and a possible broken jaw. Both patients were assessed at the scene before being taken to Princess Royal Hospital in Telford for further assessment and treatment.
“Ambulance staff said the crash had the potential to have been extremely serious, but fortunately turned out not to be too bad.â€