The incident took place last night.
The girl, with 80 per cent burn injuries, has been admitted to Bundelkhand Medical College and Hospital, said sub-inspector Mahendra Singh Dhakad of Bhangarh police station.
Sarvesh Sen (21) and another person, who is suspected to be a minor, entered the girl's house last night when she was asleep and raped her, he said.
As she cried for help, the accused poured kerosene kept in the house on her and set her on fire, he said.
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The girl's grand-father, who is very old and deaf, was sleeping outside the house when the incident took place, sub-inspector Dhakad said.
District Superintendent of Police S Shukla said that Sarvesh Sen was arrested, while the other accused, who is possibly a minor, is absconding.
A case under IPC section 376 (d) (gang-rape) and relevant sections of the Protection of Children from Sexual Offences Act has been registered.