The situation at Llanfyllin High School has been confirmed by Powys County Council, which said that a member of staff and 78 pupils were among those having to isolate.
The council said the pupil who tested positive was in Year 10, and that families with pupils that had potential contact with the student have been informed of the situation.
A spokesman for the authority said that "a focussed clean has taken place at Ysgol Llanfyllin’s secondary campus and all other pupils will continue to attend school as planned".
Councillor Phyl Davies, cabinet member for education, said: “I want to thank staff at Ysgol Llanfyllin and our education officers who have worked quickly over the weekend to minimise the risk for everybody concerned.
“We have worked with all our schools who have put measures in place to minimise the risk of coronavirus spreading. However, coronavirus is still a real threat to public health.
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“Schools have robust procedures in place and the Test, Trace, Protect process is being followed. The council has provided two face coverings to every secondary school pupil who uses home to school transport, including taxis, and they are required to wear them.
"I understand parents will be concerned but this process of testing and contact tracing is part of the ‘new normal’ and where schools follow these guidelines carefully, there is no cause for alarm.
"It is important that we all remain vigilant and maintain social distancing and continue to wash hands frequently to prevent the spared of the virus as much as we can.
"Do not send your child to school if they are unwell and have any of the three identified Covid-19 symptoms or they live in a household with someone who has symptoms or has tested positive in the past 14 days.
"We all have a part to play if we’re to avoid a spike in the county and the potential re-introduction of lockdown measures."
Parents who have further queries are being asked to contact Ysgol Llanfyllin’s senior leadership team.