Thomas said the road was in “an environmentally sensitive area”, which meant the work was “not straight forward”.
He said: “We have needed permission from landowners for the large plant that will be needed on site and, due to its size, there’s no choice but to close the road. Please bear with us.”
Journeys on the Country Bus service 359, between Exeter and Moretonhampstead, will be diverted via the A30.
Devon County Council also said it was organising a shuttle service which would operate three times a day in each direction between Dunsford and Exeter, via Longdown.