General Mills Inc. has started producing Cheerios free of genetically modified content, making the 73-year-old breakfast cereal one of the highest-profile brands to change in the face of growing complaints over such ingredients from activist groups and some consumers.

The change—which only affects original Cheerios, not other varieties like Honey Nut Cheerios—has been in the works since about a year ago, when General Mills began working to change manufacturing for Cheerios to eliminate ingredients containing genetically modified...