The incident occurred at the 'Government Girls' High School' in the town's Alaipur area on Wednesday.
bdnews24.com's Natore correspondent reported that parents and journalist did not find any of the teachers at whey they learnt of the incident.
The sick students have been admitted to the Natore Sadar Hospital.
The hospital's resident doctor, Abul Kalam Azad, said that the students are constantly vomiting.
He suspected it could be a case of food poisoning.