The school said today that all members of its boarding community were also self-isolating.
Newport's Burton Borough School said it had one pupil that had tested postive.
Principal of the Independent Oswestry School, Julian Noad, said that nine positive Covid cases had been identified within the Oswestry School community in the past week.
"As a precautionary measure, and after advice from Shropshire Council and Public Health England West Midlands, four year groups out of 14 have been asked to stay at home for 14 days. Additionally, all members of the boarding community are self-isolating for the prescribed period.
Mr Noad, said: "No school works in isolation, it is intrinsically connected to its wider community. After five weeks at school, this development comes as no great surprise; it was always inevitable that, despite stringent control measures, the virus would be seen at some stage within our community. We had contingency plans in place and Public Health England and Shropshire Council have supported our actions throughout. We look forward to quickly returning to our full and rich educational experience.
"In the meantime, we will switch to our excellent online provision for those isolating. We saw in the earlier lockdown that Oswestry School pupils thrived in their virtual learning experience.
"I am delighted to report that those identified as positive are seeing no significant ill effects and are recovering well. They can look forward to returning to a rich programme of school life very soon."
Krissi Carter, principal of Burton Borough said that the student who was tested positive had not been in school for a week and it was believed that they contracted COVID-19 through a family member.
"After discussion with the Health Protection Hub, it has been decided that there is no need for us to close any bubbles. The student has been advised that they must self-isolate for 10 days, in line with national
"Telford and Wrekin’s Health Protection Hub will be carrying out contact tracing to inform any members of the wider community who may have been in contact with the family, should they need to self-isolate.
"From everybody at Burton Borough School, we wish the student who has been tested positive and their family members a speedy recovery."