The attack took place near Vallsta Centrum a few kilometres outside Bollnäs and almost 300 kilometres north of Stockholm.
The exact extent of the man’s injuries are not yet known. Rescue officials said he was badly bitten and clawed, but his life was not in any danger.
“The man had a hunting rifle and was probably a hunter. It’s possible he shot and injured the bear, which may still be in the area,” police spokesman Hesan Akbari told news agency TT.
A team of hunters was sent out early on Thursday afternoon in an attempt to track down the bear.
Sweden is home to an estimated 2,900 bears, and the size of the population is growing, according to the Swedish University of Agricultural Sciences.
But bear attacks in Sweden remain unusual. Since 1977, there have been 26 reported attacks on people, resulting in two deaths.
It is most common for attacks to coincide with hunting expeditions, which has been the case for 19 of the 26 attacks.