The Northwest Territories Power Corporation issued a news release saying the storm caused two power outages on Sunday that affected more than half the community.
It says persistent high winds have prevented repair crews from reaching Tuktoyaktuk to fix the problem.
The community's mayor has opened a shelter at Mangilaluk School and customers who need it are being asked to make their way there if they can do so safely.
Otherwise, hamlet staff will be going door-to-door in the affected areas to help people to the shelter.
The utility says a repair crew is set to fly in on Monday as soon as the weather clears.