A Russian circus troupe were rehearsing for a performance in Bishkek, Kyrgyzstan, when the incident happened.
Workers had to drag the bear away during the attack, according to the director of the arena, Kurmangazy Isanayev.
The exits were closed off as staff waited for the emergency services.
Police shot the bear dead at the scene.
Russia has no animal cruelty laws that pertain to circuses.