The incident took place at Bareilly town, about 100 kms from here.
The victim, identified as Khushboo (18) has suffered 40 per cent burns in the attack and rushed to government hospital, they said.
According to SP Shashikant Shukla, the accused Rupali and Khushboo are students of a local higher secondary school.
"Both the girls have some old dispute. Today, they had an argument in which Khushboo allegedly passed a remark on Rupali's character," he said.
Offended by this, Rupali went to Khushboo's house, doused her in kerosene and set her ablaze, the SP said, adding the victim's mother was also injured while trying to save her.
Rupali was arrested and a case under section 307 (attempt to murder) of IPC has been registered against her, the officer added.