Nasriganj Sub-divisional Officer Ashok Kumar Jigyansu said the incident happened at Kachwa village under Karakat Police Station when students of the school reached the terrace following a rumour that a snake entered the school campus.
The overloaded terrace collapsed, injuring the students.
They were admitted to the local primary health centre and their condition was stated to be out of danger, the SDO said.
The incident will be probed and the terrace would be repaired soon, he said.