The one-vehicle smash happened on the B4555 near Highley at around 5pm on Saturday.
The fire service, police and ambulance service were on the scene. Fire crews assisted with casualty care while waiting for paramedics.
A Shropshire Fire and Rescue spokeswoman said: "At 5.01pm we received a call reporting that a road traffic collision had taken place in Bridgnorth.
"One fire appliance was mobilised from Bridgnorth. Also at the scene of the incident were the land ambulance service and the police.
"Road traffic collision involving one saloon car. No persons trapped. Crews assisting with casualty care, awaiting arrival of ambulance service."
Elsewhere in south Shropshire, a car crews were called to a car fire in Ludlow.
Shropshire Fire and Rescue received a call at 3.48pm to attend the fire at the A49 Henley Road roundabout in Ludlow.
One fire engine was sent from Ludlow station and crews assisted the owner of the 4x4 to move it to a safe area.