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. The Monona Post Office was established in 1849 and the city was incorporated May 11, 1897. In 1916, Monona contained a public house, two stores, and several mechanic shops.