Angry villagers sought revenge after discovering the body in West Bengal state, hunting down and attacking three men they accused of kidnapping, raping and murdering the girl, a police officer said.
"I am at a local hospital for the girl's post-mortem while those three suspects are also admitted at another hospital with serious injuries," Sub Inspector Shankar Das told AFP by phone.
"The situation in the local area where the incident happened is tense," Das said, referring to the villagers who were demanding that the suspects also be hanged.
Local media reported that one of the suspects had died from injuries sustained in the attack by villagers, but this could not be confirmed.
The girl had gone missing close to her home in the state's East Midnapore district on Wednesday evening, sparking a search by her concerned family and villagers, police said.
"We couldn't find the girl since last evening... Then this morning around 9:30, we were on our way out and found the girl hanging from a neem tree," an unnamed villager told NDTV news channel.
Das said he could not confirm whether the girl had in fact been raped, saying he was waiting for the post-mortem report.
India is especially sensitive to cases of sexual violence after the 2012 fatal gang-rape of a student on a moving bus in New Delhi, which led to a public outcry and tougher laws to deter rapists.
The incident in West Bengal comes after two girls, aged 12 and 14, were gang-raped and lynched in late May in northern Uttar Pradesh state, sparking renewed outrage.
In the southern city of Bangalore, the alleged rape of a six-year-old girl in a school this month triggered a series of street protests by angry parents and political activists.
India's new Prime Minister Narendra Modi has promised "zero tolerance" toward crimes against women.
But violence against women is deeply engrained in some segments of Indian society, activists say, while government crime statistics show one rape is reported every 21 minutes.
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National shame .