Some 6,800 homes were without power in Vasterbotten County, the Swedish news agency TT reported. About 2,000 households in Jamtland County and 2,400 in Vasternorrland County were also without power Monday.
A few schools in the region, including those in Wilhelmina, Lyksele, Nastansjo and Latikberg, remained closed Monday, Sveriges Radio said.
Hilde hit northern Sweden Saturday night, packing wind of over 110 mph.
Police urged drivers to use caution in the storm's wake, as numerous trees were knocked down by the strong winds.