Rexburg police are advising people to stay home and stay warm until electricity is restored.
The city is also asking residents to leave a small stream of water flowing from a faucet to avoid frozen water lines.
Police are checking on nursing homes, assisted living centers and other public facilities to make sure none are suffering medical emergencies.
The Rexburg police 911 system is working, but anyone with other weather or power-related problems is encouraged to contact City Hall at (208) 359-3020.
The 17,000 students at BYU Idaho are safe, police said, as the university has its own independent power system.