NHS Greater Glasgow and Clyde have not identified the schools or the number of cases as this would breach patient confidentiality.
A spokesperson for the health authority confirmed there was evidence of virus transmission with a small number of cases "in school settings" and that this was being "carefully managed."
Low number of cases
But the number is schoolchildren testing positive for the virus is low. On August 27, First Minister Nicola Sturgeon said that nearly 17,500 children in Scotland were tested over the preceding week and that only 49 were positive. This was only two more positive tests than the previous week, despite a 300 percent increase in the number of children tested.
The evidence of transmission in schools in Glasgow comes after the introduction of new restrictions on people visiting other households in three council areas - Glasgow, West Dunbartonshire and East Renfrewshire - with an estimated population of about 800,000.
NHS Greater Glasgow and Clyde also said contact tracing has started at Lochend Community High School and Hutchesons' Grammar School in Glasgow.
The health board said staff and pupils should still attend unless identified as a close contact.
This information emerged through the health authority's daily 4pm update to inform the public on their Test and Protect contacting tracing.
This does not mean these two schools are the same two where coronavirus has been spreading, as work is still ongoing in many schools across the city.