The incident took place when driver of the bus, carrying 30 children, lost control over the vehicle, Additional Superintendent of Police (ASP), Vidya Sagar Mishra said.
Ayush, a student of class IV, died on the spot, Mishra said.
More than 12 students were injured in the incident. They were rushed to hospital, where the condition of one student is stated to be critical, Mishra said.
An FIR has been registered against the bus driver, who is absconding, Mishra said.