Pupils have been learning online this week at Newport's Burton Borough School after 12 cases were reported up to July 3.
In a statement, Telford & Wrekin Council urged parents to book polymerase chain reaction (PCR) tests for unwell children.
The council stated: "We can confirm that the school remains closed until Monday (July 12) due to operational reasons with a number of staff having to self-isolate.
"The school is offering remote learning to all children who are at home and is open only for vulnerable learners during this time.
"Our council is in close contact with the school offering advice and support and is monitoring the situation closely.
"Across the borough, we are currently seeing an increase in cases in primary and secondary schools which reflects the national picture.
"We are urging parents and carers to please not send their children into school if they are unwell and to book a PCR test immediately even if they are experiencing mild symptoms.
"This will help schools to remain open in the run-up to the school holidays."