The girl has been identified as Mali Ahir, Dharpur, Santalpur Police Sub Inspector A B Patel said.
The injured students were taken to a nearby hospital in Dharpur, he said.
The driver of the bus fled immediately after the accident, he said adding that efforts were on to trace him.
The bus was ferrying 25-30 students and was on its way to Vauva Primary School when the mishap took place, police said.