The police had earlier arrested a teacher for the alleged sexually assault, the fourth such case in the city since July. The police say the teacher has confessed to the crime.
The director and principal were arrested under Indian Penal Code sections 188 (disobedience to order duly promulgated by public servant) and 336 (act endangering life or personal safety of others), said Additional Commissioner of Police Alok Kumar.
The child, a student of Class 1, was allegedly assaulted twice, Mr Kumar had earlier told NDTV.
The child allegedly came home and complained of pain. She was taken to a doctor who reportedly confirmed that she had been sexually assaulted. A rape case was registered on Thursday and the teacher was questioned on the child's mother's complaint.
The same day, a charge-sheet was filed in the attack on a six-year-old girl at the Vibgyor International School in July - the first case that highlighted the grossly inadequate security in schools in Bengaluru. The two gym instructors arrested in the case have been charged with gang-rape and destruction of evidence.
The government has already warned of tough action against managements flouting safety norms for children.
Chief Minister Siddaramaiah has warned school managements that permission granted to their institutions would be revoked and criminal cases filed against them if they violate guidelines for safety of children.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.