The little girl, aged between eight and 10, was found a few weeks ago in a forest in Uttar Pradesh.
Doctors said she could not communicate and displayed "monkey-like" traits.
A senior police official told BBC Hindi she had been playing with a pack of monkeys and imitating their behaviour when police went to rescue her.
The little girl was spotted by villagers in the Katarniaghat wildlife sanctuary, on the Indian border with Nepal.
The police official, Suresh Yadav, said the monkeys attacked his squad when they arrived to take her away.
Doctors said she was malnourished when she was brought in, with long hair and nails, and wounds on her body.
She was also unable to communicate but would screech and initially walked on all fours.
Her condition is said to be much better now, however, and in the long term she is expected to be handed over to child welfare agencies and other medical specialists to slowly reintroduce her to the world.
The hospital's chief medical officer, DK Singh, told BBC Hindi that although she was still in hospital, she would be transferred to the Lucknow Medical College once she had been given a clean bill of health so that she could get better medical care.
Local District Magistrate Ajaydeep Singh has also visited the girl in hospital and has named her "Forest Durga", a reference to a Hindu warrior goddess.
Many in India are comparing the little girl to Mowgli, the character from Rudyard Kipling's Jungle Book who was raised by wolves. It is not clear, however, how long the little girl has been living in the forest.