The hunter was attacked by the bear while out elk hunting with his dog in the vicinity of Hammerdal in eastern Jämtland.
The man was taken by ambulance to Östersund Hospital and the hospital later confirmed that his injuries were not life-threatening.
The man was born in 1993 and was part of a hunting party with a total of four hunters. According to Hans Ängquist, county spokesman at Östersund police, it was a female bear with two cubs who suddenly appeared and attacked the man after a dog started barking at an elk during the hunt.
Ängquist reported that shots were fired in the attack, which occurred near the village of Gåxsjö, almost 20 kilometres northwest of Hammerdal.
"The man is reported to have fired two shots," he said.
"It was one of the hunting party who called the emergency services. I know nothing about the injury situation but the man was alive when the ambulance arrived," Ängquist said.
A police patrol has inspected the site and the search for the bears has begun.