The teenager was abducted from her home in Jharkhand state on Thursday and raped in a forest while her family was away at a wedding, police said.
The victim’s family reported the attack to village council leaders who ordered two accused men to do 100 sit-ups and pay a fine of 50,000 rupees (£552).
Police said the punishment enraged the men, who beat the girl’s parents before setting her on fire.
“The two accused thrashed the parents and rushed to the house where they set the girl ablaze with the help of their accomplices,” a police spokesman said.
Fourteen men have been arrested in connection with the incident but the main suspect is still on the run, the spokesman added.
Jharkhand chief minister Raghubar Das said he was shocked by the “gruesome incident” and called for stringent action against the culprits.
India has been shaken by a series of sexual assaults since 2012, when a student was gang-raped and murdered on a New Delhi bus.
Protests have been held across the country since horrific details emerged last month about an eight-year-old girl being gang-raped and murdered in the state of Jammu and Kashmir.
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Some 40,000 rape cases were reported in India in 2016, with many more believed to have gone unreported because of stigma attached to sex crimes in the country.
The Indian government has passed a series of laws increasing punishment for rape of an adult to 20 years in prison and introducing the death penalty for anyone found guilty of raping girls aged under 12.