At least 400 pupils from Larne High School in Co Antrim have been told to remain at home.
Larne High School principal Stephen Reid told the BBC's Good Morning Ulster that the situation "isn't what we had envisaged" for the beginning of the new academic year.
He said there were "quite a few positive cases coming through to us now, quite regularly."
Mr Reid said they had spent the weekend tracing pupils who may have been in contact with positive cases, and to tell them they should not come into school.
"We have a dedicated mobile phone for parents to report Covid cases outside of school hours, and at twenty past ten last night we got our last notification on that," he said.
"In one year group we had two pupils who tested positive, but when we looked at the different classes those pupils had been through, between the two of them that meant most of the year group were close contacts and need to be tested."
Asked if he was frustrated, Mr Reid said: "I wouldn't necessarily say frustrated, because we are in the middle of a pandemic and we've got to accept there's a virus out there that none of us have control over.
"The other side of it is, we can't continue forever in a lockdown situation where children don't come to school."
However, the principal said he would like to see "clear contingency plans" from the Department of Education for the coming academic years, in terms of exams and school inspections.
