The two vehicles crashed at around 7am on Monday on the A458 at Cross Houses, at the junction for Atcham.
The road from Cross Houses down towards Much Wenlock is now shut, and motorists have been warned the closure could be in place "for some time".
Teams from Shropshire Fire and Rescue Service, West Mercia Police and West Midlands Ambulance Service have all attended the scene after being called at 7.18am.
Fire crews had to cut the car driver out, who was then handed over to the ambulance service for further care.
A spokesperson from West Midlands Ambulance Service said: "We were called at 7:18am to reports of an RTC involving a car and HGV on the A458 from Cross Houses Atcham junction.
"We sent one ambulance to the scene and have treated a man, the driver of the car, for injuries not believed to be serious. He’s been conveyed to hospital for further treatment.”
West Mercia Police Operations & Communications Centre tweeted: "Road closure – A458 at Cross Houses, Shrewsbury down towards Much Wenlock is closed following an RTC.
"This is likely to be in place for some time, please avoid and take an alternative route."