The pair were by their vehicle, parked at the Co-op off Bank Farm Road, Radbrook, at around 10.30am on Saturday when the incident took place.
A grey Hyundai Matrix reversed out of a parking space and collided with the couple, who are both in their 80s, crushing them between it and another vehicle.
The Hyundai then reportedly dragged the woman several metres and collided with parked cars before stopping.
A West Midlands Ambulance Service spokeswoman said:
“Crews arrived to find a husband and wife, both thought to be in their 80s, who had been in collision with a car.
“An off duty nurse was providing excellent first aid to the couple before crews arrived.
“The woman suffered serious facial and head injuries, arm and leg injuries. Due to the condition of the woman, the doctor anaesthetised her at the scene before she was fully immobilised and airlifted to University Hospital North Staffordshire.
“Medics were pre alerted to the arrival of the woman who was said to be in a serious condition.
“Her husband sustained serious lacerations to his face and deep wounds to all four limbs as well as a suspected chest injury.
“Crews immobilised the man with a neck collar and spinal board and dressed his wounds before conveying him by land ambulance on blue lights to Royal Shrewsbury Hospital.
“The driver of the car, a woman, was uninjured.”
PC Richard Owen who is investigating the circumstances said:
“As with all collisions where someone has been badly hurt, we will carry out inquiries to establish exactly what happened.
“I would appeal to anyone who was using the shop at the time and witnessed the incident to call us straightaway on 101.”