The collision took place on the northbound carriageway, near the Hebron junction. Police were notified at 5.50am.
The section of road was blocked for a short time while emergency services dealt with the incident, but the A1 remained open with traffic being controlled by police officers.
A Northumbria Police spokesman said: “Officers attended the scene and assisted moving the horse off the road and uplifting the vehicle.
“The driver of the car, a black Peugeot 208, was believed to have minor injuries.”