Tesco's group technical director, Tim Smith, said his company was informed of the test results by the FSAI on Tuesday and they "immediately withdrew from sale all products from the supplier in question".
In Tesco's case, two frozen beef burger products that are sold in both the UK and Ireland were found to contain horse DNA.
In a statement, Mr Smith said: "The safety and quality of our food is of the highest importance to Tesco. We will not tolerate any compromise in the quality of the food we sell. The presence of illegal meat in our products is extremely serious."
He added that Tesco was "working with the authorities in Ireland and the UK, and with the supplier concerned, to urgently understand how this has happened and how to ensure it does not happen again".
Iceland said it has "withdrawn from sale the two Iceland brand quarter pounder burger lines implicated in the study".
In a statement, the company said it noted the FSAI's findings "with concern" and "would be working closely with its suppliers to investigate this issue and to ensure that all Iceland brand products meet the high standards of quality and integrity that we specify and which our customers are entitled to expect"."