Park rangers believe the man had a "surprise encounter" with two grizzly bears that afternoon when one of them attacked, according to a press release from the National Park Service.
The man's name was not released.
Authorities airlifted the man to a waiting ambulance that rushed him to St. John's Hospital in Jackson, Wyoming, where he is in stable condition and expected to make a full recovery, the park service said.
Rangers closed the Signal Mountain Summit Road and the Signal Mountain Trail, where the attack happened.
While bear attacks are rare, The National Park Service said hikers should take precautions when hiking in areas where they live.
Rangers advise hikers to make noise as they walk, carry bear spray, hike in groups, and do not try to run away from a bear. Back away slowly if you encounter one.
If you are camping, keep all food and garbage in a sealed metal container such as a bear box or vehicle and never cook inside your tent.
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