Straits Primary School, on Longfellow Road in Lower Gornal, made the call alongside Dudley Council and the Department for Education.
It means the school will close to all pupils until November 27 and will fully reopen to all pupils on November 30.
Children will be able to learn virtually through Google Classroom and other online platforms starting from today.
A letter sent out to parents said: "After discussions with the local authority, Department for Education and the school governors, the decision has been made to close the school for two weeks due to the number of staff who have, since Thursday, reported positive tests for Covid-19.
"The levels have reached a point where we are unable to safely staff the school.
"Therefore, we will have to close the school to all pupils until November 27. The school will reopen to all pupils on November 30."