The bear, which had already sustained injuries at the weekend, was shot by county ranger Bert Ivan Mattsson.
“The bear was in good condition despite its injury and was able to chase our dog at top speed,” he told the TT news agency.
“It was a very large male, as fat and round as a ball,” he added.
With the help of hunting dog Zeuvs, Mattsson and three of his colleagues were able to keep track of the bear’s movements.
“We were hunting it for about two and a half hour before I got a chance to shoot. There was lots of scrub and dense forest,” he said.
Police said that work was underway to remove the animal from the woods and transport it to the National Veterinary Institute in Uppsala.