The woman and the child were both treated by ambulance crews after the crash south of Ludford, near Ludlow, at about 10am.
West Mercia Police asked drivers to avoid the B4361 Overton Road between Ludford and the junction towards Overton while emergency services attended the scene.
A spokesperson for West Midlands Ambulance Service said: "We were called to reports of a collision at the junction of Overton Road and the B4361 in Overton, Ludlow at 10.01am.
"One ambulance was sent to the scene and, on arrival, crews found two cars had been involved in a collision. Ambulance crews treated the passenger of one car, a woman, before conveying her to Hereford County Hospital for further assessments.
"Another passenger of the same car, a child, was assessed by the team and taken to the same hospital as a precaution. There were no other injuries."
Two fire crews from Craven Arms attended the scene, and reported that cutters were needed to help deal with the incident.
An update from Shropshire Fire & Rescue Service said: "One private vehicle in collision with one van. One casualty released by fire service using tirfor winch, now in the care of ambulance service. Assistance from Hereford and Worcester Fire Service."