The teenager was attacked on the same day and in the same eastern state of Jharkhand as a 16-year-old who was raped and burned to death.
"The girl has suffered 70 per cent first-degree burns. There is a chance that she will survive," Shailendra Barnwal, police superintendent of Pakur district, told AFP.
Police have arrested a 19-year-old man who lives in the same neighbourhood as the latest victim.
Teenager raped, burned to death in India
"He poured kerosene on the girl and set her on fire," Barnwal said.
The incident happened on Friday, the same day as the similar case in Jharkhand's Chatra district, which 15 people have been detained over.
The main suspect in the first case is said to have been angered by a village council decision that he should do 100 sit-ups and pay a $750 fine for raping the girl, and attacked the girl's parents and set their house on fire with the teenager inside.
The two cases have shone a spotlight on the treatment of rape in India, where some 40,000 cases were reported in 2016.
The country had already been agonising over the brutal gang-rape and killing of an eight-year-old girl in Jammu and Kashmir state, which is to be raised in the Supreme Court on Tuesday.
Eight Hindus have been accused over the abduction, repeated rape and killing of the Muslim girl.
Hindu activists have staged angry protests claiming that the police inquiry was biased.
Woman travels to India seeking treatment for depression, left drugged, raped and beheaded
The Supreme Court is to give a ruling on whether the flash point trial should be moved away from Jammu, a Hindu-majority region of the Muslim-dominated state.
The debate has been heightened further by new police figures indicating that more than five women were raped every day in the Indian capital this year.
As many as 578 rape cases were reported up to April 15, against 563 in 2017 during the same period, police said.
Indian authorities have faced renewed pressure to act over sexual assault since the killing of the Muslim girl in Jammu.
Amid mounting outrage, the government has changed the law to allow execution for child rapists.
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