Her parents became aware of the sexual assault after the little girl complained of stomach pain and was taken to a hospital.
Police registered the case but have not yet arrested anyone. Authorities are still trying to determine who among the multiple gym teachers and security guards at the school assaulted the girl.
One parent complained that the school "handled it very shoddily." Hundreds of parents protested the school's perceived insensitivity toward the accusation.
School chairman Rustom Kerawal addressed a parents meeting on Thursday, promising "full cooperation" in the investigation and offering his "sincere apologies."
Sexual violence against women and girls in India has sparked public outrage. On July 7, a 14-year-old girl was raped in retaliation for her brother's inappropriate behavior toward a married woman. In May, two girls, ages 14 and 16, were gang-raped and hanged in the Budaun district in Uttar Pradesh state. Protesters took to the streets to call for an end to sexual violence against women and girls.