The girl's parents informed police of the assault Friday after she was found injured Thursday inside the school in the Mangolpuri area in the northwestern section of the city, The Times of India reported.
The girl could not identify her attacker, a police official said. The male staff at the school, including teachers and a guard, was being questioned.
Residents of the area, including a number of women, staged protests in the area and in front of the hospital, charging that police were not actively investigating the case.
Some protester threw stones at vehicles and broke police barricades. Some police and residents were injured in the disturbance.
Three sisters ages 6 to 11 were raped and killed in the state of Maharashtra last month, the BBC reported.
Their bodies were found in a well two days after they were reported missing.
No one has been arrested in the incident, but a police officer was fired for not acting quickly enough after the girls disappeared from school.