Fourteen people have been arrested in connection with the attacks in the eastern Indian state of Jharkhand.
Police said the elders had ordered the accused rapists to do 100 sit-ups and pay a 50,000 rupee (£550; $750) fine as punishment.
They were so enraged they beat the girl's parents then set 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," Ashok Ram, the officer in charge of the local police station, told AFP news agency.
The girl was believed to have been abducted from her home while her parents were attending a wedding.
Local police said she was raped by two men in a forested area near the village of Raja Kendua.
Upon discovering the assault, her parents went to village elders to pursue charges against the suspected perpetrators.
Councils of village elders carry no legal weight. However, they have significant influence in many parts of rural India and are a way of settling disputes without having to go through India's expensive judicial system.
Police in the state say that they have arrested 14 of the 18 people they want to investigate with regards to the rape and subsequent murder.
One of the two men accused of carrying out the attack has yet to be arrested, Bokaro inspector general of police Shambhu Thakur told the Hindustan Times.
However, several village elders have been charged with passing unlawful orders and tampering with evidence.
The latest incident comes as India reels from a string of violent sexual crimes.
About 40,000 rape cases were reported in India in 2016. Many cases, however, are believed to go unreported because of the stigma that is attached to rape and sexual assault.
(The latest incident comes as India reels under a string of violent sexual crimes)