Monona is a city in Clayton County, Iowa, United States. The population was 1,471 at the time of the 2020 census. The name Monona is of A…Monona is a city in Clayton County, Iowa, United States. The population was 1,471 at the time of the 2020 census. The name Monona is of American native origin. In 1916, Monona contained a public house, two stores, and several mechanic shops.