Both Jesson's CE Voluntary Aided Primary School and St Joseph's Catholic Primary School will not reopen now until after half-term.
Jesson's will reopen on November 3, while St Joseph's is due to reopen on November 2.
In a statement on St Joseph's website on Friday, it states: "School is currently closed due to a number of positive Covid-19 cases. School will re-open on Monday, November 2."
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A letter sent to parents from Jesson's headteacher Sarah Lea, said: "As you are well aware and despite all our measures to reduce infection, several members of our school community have tested positive for Covid-19.
"We have continued to work with Dudley Public Health Office 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 governing body, the diocese and the local authority, I have decided to make the decision to close the school from 3.30pm on Friday, October 16, and I will reopen on Tuesday, November 3.
"Please be assured that 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."