North Lanarkshire Council officials confirmed horse DNA had been found in a frozen burger supplied to the school.
The meat had been supplied by the Brakes Group.
Tests out on Thursday revealed the presence of horse DNA and procurement agency Scotland Excel advised councils to suspend the use of frozen beef burgers. That has now been extended to all beef products.
A council spokesman said: "We can confirm the frozen burger found to contain horse DNA on Thursday was supplied by Brakes Group to Cumbernauld High.
"It is unacceptable to the council that a supplier would supply a product containing horse DNA to one of our schools.
"We cannot confirm these products have not been consumed. However, the consumption of horse meat is not considered harmful to health.
"This is a consumer confidence issue: when we buy a product we expect it to contain what it says on the label.
"We will continue to take any action necessary to ensure the integrity of the food supplied to our establishments."
It will still "carry out additional testing in the coming days".
Scotland Excel, which deals with contracts on a national basis, recommended councils and other public-sector customers to take a "precautionary approach" and take all frozen beef products off the menu.
A spokesman for Brakes said: "Until we are able to ascertain the facts, we have placed the beef burger on hold as a precaution.
"All customers are being contacted to ensure they hold the product in a segregated area while we and the Food Standards Agency continue investigations."