The power outages have been caused by the short circuiting of power lines in rural areas following heavy snow falls on Friday and Saturday in northern areas of Sweden.
According to state-owned utility Vattenfall around 3,000 of its customers remained without electricity on Sunday morning.
The firm has assigned 100 staff to work with finding and correcting problems with power lines and supplies over the weekend. The firm has on Sunday reinforced this workforce with staff from other areas of Sweden.
Most of the affected households were in the province of Norrbotten but also in Västerbotten and Västernorrland there were reports of power outages.
Eon reported that it has managed to return supplies to most of its customers and only a handful remained without electricity on Sunday morning.
Fortum confirmed on its home page on Sunday morning that all of its customers had regained access to electricity supplies.
The Swedish meteorological agency (SMHI) forecast milder weather and higher temperatures over the next couple of days with a thick layer of cloud over most parts of the country. More snow and rain is forecast in central areas of Sweden from Wednesday to Friday and the windy weather is expected to continue over next weekend.