The Wensleydale School has told three year groups to work from home for two weeks following another Covid-19 case.
The school said it was facing “significant operational difficulties” after a third positive test at the school.
Headteacher Julia Polley said in a letter to parents: “We have been made aware that a further member of our school community has tested positive for Covid-19.
“We know that you may find this concerning, but we are continuing to monitor the situation and are working closely with Public Health England.”
Mrs Polley added: “The third confirmed case this week has presented us with significant operational difficulties, due to the number of staff self-isolating.
“In total, 16 members of staff are now self-isolating, across all our staffing groups – teaching, support and cleaning.
“This causes a health and safety and safeguarding issue for the school in terms of required staffing levels and site cleanliness.
“The reduction in the capacity of our cleaning staff for example, means that operationally we must also reduce the number of rooms in use for the time being, in order to keep those students and staff still in school safe.”
The head said that although this meant the school remained open, it would only be open for Key Stages 4 and 5 until Monday, November 30.
The school said students in Years 7, 8 and 9 would work remotely from home until the school fully reopened.
“From Monday, November 30 staffing levels will return to a manageable level and we will be in position to welcome Key Stage 3 students back into school from that date,” Mrs Polley said.
