Several pupils have been sent home to self-isolate for 14 days after the school was informed of the case by Public Health England.
In a letter to parents and carers, school headteacher Rupert Moreton said: “We have been advised by Public Health England that there is a confirmed case of Covid-19 within the school.
“We are continuing to monitor the situation and are working closely with Public Health England.
"This letter is to inform you of the current situation and provide advice on how to support your child. Please be assured that for most people, coronavirus (Covid-19) will be a mild illness.
“The children who have been in direct prolonged contact with the confirmed case have been informed and will be staying at home for 14 days.
“The school remains open and, providing your child remains well, they can continue to attend school as normal. We will keep this under review.”
Malmesbury School is one of several secondary schools in north and west Wiltshire to report a positive case of the coronavirus.
Sheldon School in Chippenham, St Augustine’s Catholic College and John of Gaunt School in Trowbridge, St Laurence School in Bradford on Avon and Warminster School have all sent hundreds of pupils home to self-isolate in the past week or so following the return to school in early September.