The incident was reported in the city of Vasco da Gama on Monday, sparking a massive manhunt to trace the accused, thought to be in his early 20s.
"The girl was raped inside the school toilet during recess," a police official said, requesting not to be named.
He said the toilet was situated next to the principal's office at Deepvihar High School, which has a primary section.
Thousands of people surrounded the school on Monday night demanding the arrest of principal and the perpetrator, who is yet to be found.
The principal, whose name has been withheld to protect the girl's identity, was initially detained and later arrested for alleged negligence of duty, the police official said.
The arrest comes after the gang rape of a student on a bus in New Delhi last month sparked nationwide protests and fuelled anger across India over the alarming incidence of sexual assault.
Five men and a teenager have been charged with the rape and murder of the 23-year-old woman, who died 13 days later in a Singapore hospital from horrific injuries.
Also in Goa on Monday, a police officer was arrested accused of sexually abusing sex workers, who said he and two other police officers all now suspended had been sexually exploiting them in return for protection of their trade. – AFP