The electricity companies are hoping that most of the households will have power back again by Monday night, but that some will have to wait til tomorrow.
Ann-Nina Finne at Eon said to Swedish Radio P4 Kronoberg it has mainly been Jönköping and Kalmar counties that were affected.
But thousands of homes in Västra Götaland and Halland counties have also been without power.
And around 10,000 telephone lines for Telia customers were cut.
The nuclear reactor at Ringhals, north of Varberg, also had to be shut down, because of the amount of water that was coming through the back way into the floor drain, reports news agency TT. Gösta Larsen, head of information at Ringhals, told Swedish Radio P4 Halland that it was not a serious problem with regards to reactor safety, but that it's affecting productivity for a few days, which isn't good, he said.