The accused poured kerosene and set the girl on fire last evening when she was returning from fields, they said.
She sustained serious burn injuries and was rushed to a hospital, from where she was referred to another hospital in Allahabad in a serious condition, they said.
Police said a land dispute is prima facie the reason for the incident.
The girl's father filed a complaint an FIR was registered against Om Prakash Maurya, his wife and two others, they said.