NHS Greater Glasgow and Clyde said eight new positive cases identified included pupils from Bannerman High School in the suburb of Baillieston.
A statement from the health board said none of the cases were experiencing anything but mild symptoms.
“The school reopened today but none have actually attended as they are self-isolating at home," the health board said.
"Test and Protect staff are contacting anyone who may be affected and there is no current added risk to the wider community due to this cluster of cases.”
The cluster comes as the Scottish government has pushed for all schools to fully reopen by 18 August after almost five months of students being away from classrooms.
Anne Longfield, the children’s commissioner for England, called on Sunday for pupils and teachers to be tested weekly, but ministers have ruled out routine testing for people without coronavirus symptoms.
Dr Linda de Caestecker, the Glasgow board’s public health director, said the new cluster of cases was being “thoroughly investigated”.
“All settings that these cases attended during their infectious period are being identified, assessed and are being supported with control measures, and anyone who may have been exposed to these cases is being given appropriate advice,” she said.
“Anyone affected will be contacted through the Test and Protect service."
Dr de Caestecker added: “We want to reassure the wider community and especially pupils and teachers returning to school that there is no added risk due to this cluster.
“We also want to remind people to stay off school or work and get tested if they experience any symptoms.”
David Linden, MP for Glasgow East, said he had spoken to the school and health officials to better understand the details of the cluster.
“First and foremost, public safety is the number one priority and I am reassured that all pupils who tested positive did not attend school today,” Mr Linden said.
“I will continue to work with the education authorities and the health board to ensure this situation is managed and that parents can have confidence in sending their children to school.”
Additional reporting by PA