Veterinarians attending the animal were set to administer a lethal dose of anaesthesia ahead of the mercy killing when the 70-year-old breathed her last.
Arundhati broke her front left leg about three weeks ago while she was being taken for a walk by her keeper in the Chilla forest range, about 60 km from here.
The animal was unable to stand on her legs and was in tremendous pain.
A team of veterinarians from the forest department and the Wildlife Trust of India reached the spot late in the evening to administer the anaesthesia but the animal passed away before they could do so, an official said.
Earlier, animal rights organisations had demanded better care for the animal, but finally agreed with the veterinarians that euthanasia was the only option left to relieve her from pain and distress.