The car flipped onto its roof after hitting a bollard on Priorslee Avenue, by the turning for Brookvale Road, in Telford, on Thursday.
Shropshire Fire and Rescue and West Midlands Ambulance Service were called to the crash just after 11am.
Fire crews sent one appliance from Telford Central to reports of a crash with no persons trapped.
The ambulance service sent an ambulance to treat the woman who suffered a shoulder injury and minor leg injuries.
The woman, in her 20s, was taken to Telford's Princess Royal Hospital.