The road between Beaminster and the A356 was closed due to the fire in White Sheet Hill at about 22:45 BST on Sunday.
Dorset Police said it was still trying to locate the driver.
Dorset Council arranged for the burnt-out vehicle to be removed on Tuesday.
The outage also knocked out phone lines, affecting schools, a GP surgery, businesses and people working from home.
Dorset councillor for Beaminster, Craig Monks, said: “We will need to ask questions on how this was allowed to happen and how resilient our connection is.
“The internet is vital to residents and businesses.”
Openreach said it reviewed all incidents to see if lessons could be learned.