The man approached the calf after it became separated from its mother when the bison herd crossed the swollen Lamar River in the northeastern corner of the Wyoming park, the NPS said.
He then pushed the struggling calf up a river bank and onto a roadway.
Witnesses said the man and other tourists patted the “noticeably distressed” and shivering baby bison, the Cowboy State Daily reported.
The calf and mother were seen calling out to each other from opposite sides of the river, the news site reported.
Park rangers’ attempts to reunite the calf with the herd were unsuccessful, and the calf was euthanised after it caused a “hazardous situation” by following cars and visitors, the NPS said.
Yellowstone regulations state that visitors must remain at least 25 yards (23m) away from all wildlife including bison, elk and deer, and at least 100 yards (91m) away from wolves and bears.
Park rangers recently appealed to tourists to stay clear of wild animals after several documented incidents of bison being approached for selfies or pets.
“Approaching wild animals can drastically affect their well-being and, in this case, their survival,” an NPS spokesperson said.
The tourist is described as a white male in their 40s or 50s, who was wearing a blue shirt and black pants.
Anyone with information is asked to contact the Yellowstone National Park Tip Line at 307-344-2132 or email YELL_Tip@nps.gov.