All Year 9 pupils – 284 – are being asked to self-isolate for 14 days until 25 September.
The schools says it is a precautionary measure and the pupils will continue learning at home.
The news came the same day parents of Year 5 pupils at Lainesmead Primary School were asked to go and collect their children after a youngster tested positive.
Headteacher Anita Ellis, said: “We have written to all parents and carers to explain the situation, and we really appreciate their understanding and support as we know this will cause some unfortunate disruption for the Year 9 pupils and their families.
“The safety of everyone within our school community is our top priority and we’ll continue to work with Wiltshire Council and Public Health England to ensure this is managed closely and that the rest of the school can continue as before.
“We look forward to welcoming everyone back in a couple of weeks.”
Kate Blackburn, director of public health for Wiltshire, said: “It’s important this very precautionary action is taken so that the risk of any transmission within the school community is as low as possible. We’ll work with Public Health England to support
the school as much as possible so that their high standard of COVID-19 measures are maintained.
“Anyone that is asked to self-isolate should adhere to the government guidance; if they don’t have symptoms, they do not need to get a test. However, if a member of their household has symptoms and takes a test then they should self-isolate.
“We ask that people regularly wash hands, maintain social distancing and wear face coverings where appropriate – this is the best way to keep you and everyone safe as much as possible.”
Mike Wade, deputy director for health protection at Public Health England South West, said: “PHE South West is working closely with the school to provide public health advice to stop the virus spreading.
“Everyone should be following social distancing advice to prevent the spread of the virus in schools.
“Good hygiene is the best prevention and there are some simple steps you can take to protect you, your family and colleagues by washing your hands regularly and thoroughly and if you cough, cover your mouth and nose with a tissue.”