The cases were reported during the last two days at the school and junior college in Wyra town, officials said.
The school authorities conducted tests for all students after a couple of students showed suspected symptoms.
Worried parents rushed to the school and took their wards home. District Medical and Health Officer Dr B. Malathi said those who tested positive were fine.
The official said the students who tested positive were taken home by their parents for home quarantine and they were all fine.
The parents of students who tested negative also took them home as a precautionary measure. Some parents pulled up the school authorities over the delay in giving them this information.
This is the first time since the reopening of residential schools in the state last month that such a large number of students tested positive.
The incident prompted the authorities to ramp up Covid-19 preventive measures in residential schools.
Senior officials from various departments visited the school and asked the school authorities to ensure strict adherence to preventive measures like maintaining social distance, wearing of masks and use of sanitiser.
About 550 students are studying in the school and junior college. Some parents said that overcrowding led to the Covid spread.
For 450 students studying from class 5 to 10, there are only 16 rooms. Forty students sleep in every room after the classes.
The dining hall has a capacity for only 200 students.
School principal Lakshmi said the proposal for construction of more buildings was pending with the authorities.
Educational institutions in Telangana reopened from September 1. However, the high court allowed reopening of residential schools in the last week of October after the education department gave an assurance that all preventive measures will be taken.