The black BMW and lorry collided on the B4176 by the roundabout and Shell garage in Sutton Maddock shortly before 6am, forcing the closure of the road.
West Mercia Police urged people to avoid the area while the road was closed while crews from West Midlands Ambulance Service and Shropshire Fire & Rescue Service also attended the scene.
Four fire appliances were sent from Telford at 5.59am, with an operations officer also in attendance.
A spokeswoman for West Midlands Ambulance Service said one ambulance and a paramedic officer were sent to the scene, where they found the injured BMW driver out of the car.
"On arrival crews discovered a car and a lorry had been involved in a collision," the spokeswoman said. "Ambulance crews assessed him for minor injuries before conveying him to Princess Royal Hospital for further treatment. The driver of the lorry was not injured."
A passer-by on his way to work helped the BMW driver out of the car while another called the emergency services. It's understood the BMW was partially stuck under the lorry, making the doors hard to open.
The fire service added: "This incident involved a car and a lorry which had collided and required making safe. No persons trapped," and crews were stood down at 6.16am.
West Mercia Police has confirmed the road has been re-opened.