By 4.30am on Monday, 13,000 households had lost their electricity supply.
“All of our staff will be deployed to repair the power lines after the storm,” said Johan Aspegren, a spokesman for Eon.
The storm caused a fatal accident in Tingsryd on Sunday night. A 31-year-old man died after going outside to remove a fallen tree.
A passer-by found the victim trapped under a tree shortly after midnight. A second tree had fallen on top of him while he was attempting to clear away the first.
There were few other reports of storm damage in southern Sweden.
“Just some scaffolding in central Malmö that has blown down. Nobody was injured,” said a police spokesman.