The animal was shot around two kilometres from the spot near Valsjöbyn where the hunter’s body was found on Monday.
“We’re not entirely sure but we believe it’s the same bear that killed the hunter,” said police spokesman Bengt Stadin.
Bear-related deaths are rare in Sweden, the last two coming in 2004 and 1902.
In 2004 a 40-year-old hunter was clawed to death by a female bear outside Jokkmokk. The bear was shot a few days.
A bullet wound found on the animal’s body suggested that the hunter was killed after firing a shot at the bear.