Perry Hall Primary School, in Wednesfield, confirmed that all staff and pupils within the year six bubble were now self-isolating.
The school was informed of the positive case of coronavirus within the school on October 12.
A spokesman for the school said: "After receiving notification of a positive case of Covid-19 within school on October 12, we immediately contacted both Public Health England and the Department for Education coronavirus helpline.
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"Advice given was that all staff and pupils who have had direct contact with the affected person should isolate for 14 days. This affects all adults and children within our year six bubble, who will only need to get a test if they experience any symptoms of Covid-19 during the isolation period. Siblings of year six pupils do not need to isolate and the rest of the school will remain open as normal.
"The likelihood of an outbreak in the affected bubble is low, however we must follow the guidelines and act quickly to protect everyone in our school community.
"We have also been in touch with the local authority who have been very supportive, and are satisfied that we have acted carefully to ensure that those who have been within our school provision can be safe at this time.
"With the reported increase in Covid-19 cases, our school were already preparing for such an event. We have been working on our Office 365 digital learning platform, and year six pupils are currently taking part in ‘live lessons’ from home delivered by their teachers. School is also providing home learning packs to support families that have difficulties accessing the internet.
"We would like to thank our parents and staff for all of their support."