Parents of four children at the school in Bangalore complained that staff cut off tufts of their hair and denied them the same uniform as other students.
The children are reportedly from low-caste Hindu communities, enrolled under a recent anti-discrimination law.
There has been no response so far from the school itself.
A senior official in the Karnataka state department of education, Kumar Nayak, told the BBC that an inquiry was under way.
"Necessary action will be taken if the charge is proved," he said.
Indian schools are supposed to reserve up to a quarter of their places for children from poorer backgrounds.
