They have warned visitors to keep their distance from wildlife for the safety of both humans and animals.
The bison was rejected by its herd after contact with the people.
The park said it was just one example of "inappropriate, dangerous and illegal behaviour with wildlife".
Other such behaviour included petting bison and taking selfies with them.
The visitors had what the park described as a "misplaced concern" for the calf.
They saw it on its own and tried to bring it to a park facility.
But their action led to the calf's mother rejecting it, and despite rangers' repeated attempts to bring it back to the herd, it started "causing a dangerous situation by continually approaching people and cars", officials said in a statement.
"Approaching wild animals can drastically affect their well-being and, in this case, their survival."
Social media users reacted to the news with anger and sadness.
There are about 5,000 wild bison, also known as buffalo, in Yellowstone National Park. There are also bears and wolves.
At least five tourists were hurt in the national park last year after getting too close to animals, leading the park to put out a warning on human safety grounds.
Tourists are warned to stay at least 25 yards (23m) away from all wildlife and at least 100 yards away from bears and wolves.
Officials at the famous Yellowstone National Park in the US have revealed that they had to put down a newborn bison after some tourists put it in the boot of their car.