The collision happened in Harlescott Lane on Wednesday afternoon.
A West Midlands Ambulance Service spokesman said: "We were called to reports of a collision between a car and a van at the junction of Ellesmere Road and Harlescott Lane at 1.41pm. One ambulance attended the scene. On arrival we discovered two patients. The driver of the car, a woman, was assisted out of the vehicle by colleagues from the fire service. She was treated for injuries not believed to be serious before being taken to Royal Shrewsbury Hospital by land ambulance. The van driver was assessed and discharged at the scene."
A Shropshire Fire and Rescue spokesman said: "At 1.50pm on Wednesday, July 27, SFRS Fire Control received a call reporting that a road traffic collision had taken place in Shrewsbury. Two vehicle road traffic collision, two casualties left in the care of the ambulance.
"Two fire appliances were mobilised from Shrewsbury."
Crews used small gear to deal with the incident.