Burns, a 25-year Saatchi & Saatchi veteran, left the agency last month. Three days later, 17 employees on the General Mills account resigned.
The team has since been hired by Interpublic to work in a children- and family focused health-and-fitness marketing arm.
"Saatchi & Saatchi has commenced a lawsuit against Michael Burns in the Supreme Court of the state of New York," the agency said in a statement.
"The lawsuit seeks damages and other relief against Mr Burns. Upon advice of counsel, we will have no further comment."