Q3 Academy Tipton sent a letter to parents on Monday confirming the positive case.
The self-isolating students can return to school on September 28.
The letter says: "We have been advised by Public Health England that there has been a confirmed case of Covid-19 within the school.
"We know that you may find this concerning but are continuing to monitor the situation and are working closely with Public Health England.
More Covid-19 coverage:
"This letter is to inform you of the current situation and provide advice on how to support your child.
"Please be reassured that for most people, coronavirus (Covid-19) will be a mild illness.
"The small number of children who have been in direct prolonged contact with the confirmed case will have received an individual letter and will be staying at home for 14 days.
"The school remains open and your child should continue to attend if they remain well."