Slavka Sekulovic, 58, had put her arm into the cage with two Siberian tigers when one of them grabbed it and bit it off, said doctor Zoran Srzentic who admitted the woman at a nearby hospital.
Srzentic said that Sekulovic's life is not in danger, though she remained in shock after losing a lot of blood.
"The tiger just wouldn't let it go," he added.
The tigers were brought into Montenegro last year from Bosnia. The authorities initially had detained three people on suspicion of smuggling the animals — which are considered endangered species — but no formal charges were raised.
The owner, Stojan Sekulovic, has claimed the tigers were a present for his private zoo.