Western Power Distribution say the fault is ongoing but say power will be restored to all homes within an hour.
A spokeswoman said: "The fault initially occurred just after 3pm and affected a number of areas in and around Barnstaple including Fremington and Bickington.
"We are switching people to an alternative supply while we locate the fault. At this stage we don't know if it is overground or underground."
She added: "Our primary concern is getting people back on supply. Customers are being switched back on in phases and everyone will be back on within the hour."