The incident happened at about 22:45 on Monday on the A713 Castle Douglas to Ayr road just north of Parton.
A Daf lorry, part of a convoy heading to the Brockloch wind farm at Carsphairn, left the roadway.
Nobody was injured in the crash but the route is expected to be closed for a considerable length of time.
Insp Campbell Moffat said: "The road is fully closed at present and will remain so until the heavy lifting equipment can be taken to the crash site to recover the vehicle and load.
"A full diversion has been implemented around the scene and drivers are asked to avoid the area where possible."
A road in southern Scotland has been completely blocked after an accident involving a lorry towing part of a wind turbine.