RSA Academy, in Bilston Road, confirmed it would close on Friday afternoon, and would not reopen until Monday, November 2.
A letter from senior vice principal Helen Tanner, seen by the Express and Star, states: "As you are well aware, and despite all our measures to reduce infection, several staff and students of our school community have tested positive for Covid-19.
"For families directly affected by these cases, we know that self-isolation and disruption to your child's learning has caused you worries on many levels.
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"We also under that, even if your child has not been asked to self-isolate, the growing concern about increasing cases in school is causing anxiety and disruption for everyone.
"We have continued to work with Sandwell Public Health and I believe that if we do not respond quickly, we will be facing a much larger problem.
"In light of this information and after seeking approval from our local governing body board, our trust and the local authority, I have made the decision to close the school from 3.30pm on Friday, October 16, and will reopen on Monday, November 2.
"Please be assured this decision has not been taken lightly, we have taken all family circumstances into consideration but strongly believe that this is the most effective yet least disruptive action we can take."