The incident occurred in K G Halli police station limits in the intervening night of yesterday and today, police said, adding, the girl was found by beat police patrolling the area.
The girl with bleeding head injuries was immediately rushed to the state-run Bowring hospital, officials added.
She has suffered several injuries.
Doctors treating the girl suspect she has been sexually assaulted and said she is currently under shock.
"The girl was admitted at about 3.45 AM at ourhospital. There are genital injuries like vaginal tear, herring finger had been amputated... There is also A scalp injury andshe is bleeding," Dr Manjunath told reporters here.
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Stating that all her other health parameters arestable, doctors said the child is out of danger and isundergoing treatment at the paediatric intensive care unit.
Additional Commissioner of Police (Bengaluru) Hemanth Nimbalkar said a case has been registered under Protection of Children from Sexual Offences Act (POCSO) and investigations are on.
He said three teams have been formed, including a technical team and a special team under the supervision of Ajay Hilory, Deputy Commissioner of Police (Bengaluru East).
Following her statementa case was registered.
Nimbalkar quoted the mother as telling police that her daughter had gone out of the tent in which they were staying to attend to nature's call and did not return.
"We can get to know about the incident and who took her.. all those things, once the girl is fully conscious,"he added.
Police suspect someone known to the girl or someone residing near her house might have committed the crime.
Minister for Bengaluru Development and Town Planning KJ George who visited the girl at the hospital called it a "heinous crime" and said the incident shames the entire society.