Granite Falls is a city located mostly in Yellow Medicine County, Minnesota, of which it is the county seat with a small portion in Chipp…Granite Falls is a city located mostly in Yellow Medicine County, Minnesota, of which it is the county seat with a small portion in Chippewa County, Minnesota. The population was 2,737 at the 2020 census. The Andrew John Volstead House, a National Historic Landmark, is located in Granite Falls. Another NHL located in Granite Falls is the Julian A. Weaver House.