Other visitors intervened by shouting and clapping to scare the bison away until emergency personnel arrived.
Park paramedics initially transported McDaniel to a local hospital before transferring him to Bozeman via a two-hour ambulance ride.
"All the people that were there were amazing," McDaniel told CNN. "They were all positive – they were trying to help as best they could."
The photographer who filmed the incident, Mike MacLeod, noted that the bison appeared highly agitated prior to the confrontation.
He also confirmed that the victims maintained a respectful distance and did not provoke the animal.
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National Park Service confirmed the emergency response but declined to provide additional details regarding whether the bison's behavior was linked to the ongoing mating season, which runs from June to September.