The video purportedly showed the class three students standing nude under the sun with their hands up.
Ordering a probe into the incident, Chittoor district collector PS Pradyumna has said stern action would be taken against the management.
A woman teacher had allegedly awarded the punishment to the children Thursday for not completing their home work, a district education department official said.
If proven guilty, the government recognition given to school would be revoked, he said.
Meanwhile, based on the complaint by parents of the students, police have registered a case against the Chitanya Barathi English Medium School, police said.