The man had been tracking a deer when he was set on by the grizzly at around 1.45pm near the Yellow Mule Trail, just south of the town of Big Sky, Gallatin County Sheriff Search and Rescue said in a statement.
Emergency crews raced to the remote area about 55 miles north of Yellowstone National Park after a member of the hunting party called 911.
The injured hunter was transported by air rescue helicopter to Bozeman Health Deaconess Regional Medical Center, officials said. His condition has not been released.
The US Forest Service said it had implemented an emergency closure of an area around the Buck Ridge and Yellow Mule as it searched for the bear, which may have been shot.
Gallatin County Sheriff Dan Springer said in a statement it was crucial for hunters to have a contingency plan for when traversing backcountry areas.
The 10-year-old female grizzly and her cub smashed a kitchen window at a home near the town of West Yellowstone on 2 September and stole dog food, the Montana Fish, Wildlife and Parks said in a statement.
Wildlife officers captured the cub and shot the adult grizzly dead later that evening after receiving clearance from the US Fish & Wildlife Service, due to grizzlies’ protected status under the Endangered Species Act.
In a separate incident, two anglers shot and killed a grizzly after it charged at them in the Flathead National Park on 29 August.
Encounters between grizzlies and humans are becoming more frequent as the bear population increase.
“This time of year is when bears are active for longer periods as they consume more food in preparation for hibernation. This period overlaps with hunting season and other fall recreation activities,” the Montana Fish, Wildlife and Parks said.