Emergency crews were called to an address in Kingswood Road, Mytton Oak, shortly after 7pm on Monday.
She was freed by the fire service and given oxygen therapy until a paramedic arrived.
Jamie Arrowsmith, of West Midlands Ambulance Service, said: "We were called at 7.03pm to reports of a patient who was trapped between a car and a wall on Kingswood Road. One ambulance and a paramedic officer attended the scene.
"On arrival we discovered one patient, a woman, who was treated for a potentially serious injury before being transported to Royal Shrewsbury Hospital."
In a separate incident, an ambulance and firefighters were called to an address in Third Avenue, Ketley Bank, Telford, at 5.16am today to a medical emergency.
They arrived to find a man requiring treatment at the scene before paramedics transported him to the Princess Royal Hospital, in Telford, for further assessment.