The accident on the A488 Old Shorthill Lane between Lea Cross and Cruckmeole happened at about 5pm on Thursday.
West Midlands Ambulance Service said two ambulances and a paramedic officer attended the scene.
"Crews discovered two patients on their arrival. The driver of one of the cars, a woman, had got herself out of her vehicle and was treated for minor injuries before being taken to Royal Shrewsbury Hospital.
"The second patient, a man, was discharged on scene with minor injuries," the service said.
The road was closed by West Mercia Police following the collision, resulting in congestion in the Hanwood area.