The collision, which involved just one vehicle, happened on the A6106 Millerhill Road at about 1:30pm.
The road was closed for more than two hours - reopening just after 4pm - and there have been several reports of traffic delays in the area.
A police spokeswoman said the vehicle came off the road and a man was taken to hospital.
It is understood the car struck an obstacle, forcing it to turn on its side.
Details on the extent of the man's injuries and his condition are not known at this stage.
A fire service spokeswoman said earlier that cutting gear was used after two fire appliances were sent to the scene.