Year 8 students at the Charlton School in Wellington will not be at school next week after a teacher contracted the disease.
Eight staff members are now self-isolating as a result.
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Meanwhile Southall School in Dawley has sent a group of children home after a member of staff tested positive.
At least five schools in Shropshire have now been affected by outbreaks of coronavirus.
A Charlton School spokesman said: "A case of Covid-19 has been confirmed involving a member of staff.
"All students in the classes of the teacher have been advised to self-isolate for 14 days from the last day they were taught by them.
"A total of eight members of staff have been advised to self-isolate as a result, which means the school will not be opening for Year 8 pupils on Monday and will remain closed to them until Friday October 2, unless the staff are able to return sooner.
"All other year groups at the school, other than for students in self-isolation, will be running as usual, and Year 8 students will return as soon as staff are available.
"Telford & Wrekin Council’s health protection hub is contacting all those affected, in line with government guidelines."
Dr Gill Eatough, chief executive of the Learning Community Trust, which Charlton School is part of, said: “All our Covid systems are in place, and we have been following all government guidance to the letter.
“This Covid-19 case was contracted by a member of staff from a contact outside of the school, and we have acted as swiftly as possible to tackle the situation.
“The number of staff having to self-isolate as a result of this case means we are unable to staff our year eight classes, so we have been left with no alternative but to close these until the isolation period is complete.”
Southall School, which caters for students aged 11 to 16, said that it has contacted all parents of children who were in direct contact with the individual who tested positive.
Those children who have been asked to self-isolate can return to school in 10 days' time, on September 28.
A school spokesperson said: "We can confirm that there has been a case of Covid-19 involving a member of staff at Southall School in Dawley, Telford.
"As a precaution, a number of children and other members of staff who have identified as contacts of the staff member have been sent home in order for them to isolate.
"The school remains open for the remaining staff and pupils. Telford & Wrekin Council and the school are monitoring the situation."
Captain Webb Primary School has also seen children sent home after one tested positive.
Individual students at Shrewsbury Academy, Haberdashers Adams Grammar in Newport, St Mary's CE Primary School in Albrighton and Ysgol Llanfyllin in Powys have also returned positive tests.
Meanwhile a survey has found that more than four in five schools in England currently have children not in class because they cannot access a Covid-19 test.