The agency predicted winds of 24m/s to 28m/s in both Jämtland and Västernorrland.
SMHI warned that the strong winds would make it very difficult to even stand upright, urging skiers to stay off the mountains. It added that the winds could reach hurricane strength.
Temperatures are expected to reach -8C.
The area has seen heavy snowfall in recent days, with experts warning that the strong winds could also cause avalanche risks.
The agency issued a less severe class-one warning for the southern reaches of Sweden, where storms are expected to pass through over the weekend.
Ekstremveret #Cora er no over i fase C. Les heile varselet her https://t.co/CUh4nogBgT pic.twitter.com/tWIVO1XXUN
— Meteorologene (@Meteorologene) January 7, 2018
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