A grizzly bear that killed a man and injured two other people at a campground in Montana was euthanized on Friday and her three yearling cubs will be sent to a zoo, officials in the northwestern US state said.

Rangers on Wednesday found the mauled body of Kevin Kramer (48) at Soda Butte Campground in the Gallatin National Forest, on the northeastern border of Yellowstone National Park.

Two other campers, a 58-year-old woman and a 21-year-old man, were also injured by a bear at the same park. The three campers were asleep when they were set upon.

Montana Fish, Wildlife and Parks officials said trackers in the vicinity captured a mother bear and her three cubs suspected of carrying out the attacks.

"Bear hair, saliva and tissue samples collected by investigators and tested by a DNA identification lab... confirmed that the captured adult bear was responsible for the attack," the US Fish and Wildlife Service (USFWS) said in a statement.

The adult bear was euthanized in accordance with rules which call for "grizzly bears that display unprovoked aggressive behaviour toward humans, or that cause substantial human injury, including loss of human life, be removed from the population."

The USFWS said the euthanized bear will be submitted to an autopsy.

"We want to find out if the unusual predatory behaviour of this bear on humans is related to any physical condition or ailment," said USFWS official Chris Servheen, adding that an autopsy was "the only way to determine this."

Bear attacks on humans are rare but not unheard of in the United States, notably in the country's heavily traveled national parks where the wild animals can become attracted to food brought in by visitors.