The school named "Kidzee Vidyalaya" is situated in the campus of the Indian Oil Corporation at Barauni.
"A complaint has been lodged by the father of the girl and we are looking into the matter," In-charge of Town police station Mohammad Islam said.
Islam said the girl's father had also complained to the IOC management about the incident which occurred yesterday.
As per the complaint, the hair of the minor girl was cut on the instruction of the school principal.