When they arrived, they found an injured man who was already out of one of the cars but a woman was still trapped in the other.
A spokesperson for Dorset and Wiltshire Fire and Rescue Service said: "Crews extricated the female and left her in the care of the ambulance service. Both vehicles were made safe and the incident was handed over to the police who were on scene."
Officers from Chippenham Police and Royal Wootton Basset and Cricklade Police closed the road until 12.12pm to clear the area and have the cars recovered.
South West Ambulance Service took one motorist to Great Western Hospital with a minor injury and took another to hospital for a more in-depth assessment.