The students were aged between eight and 16, police said.
Parents were said to have gathered outside the school to hear of the condition of their children.
The government said that it had ordered an investigation into the incident.
Ved Marwah, a former New Delhi police commissioner, told Al Jazeera: "It was raining from last night. An examination was on [when] a rumour went around that there was a short-circuit and that the place was on fire.
"The teachers told the students to get out and the students just rushed. And there was one staircase and in that ... five students died."