Munden is a city in Republic County, Kansas, United States. As of the 2020 census, the population of the city was 96. Munden was foundeā¦Munden is a city in Republic County, Kansas, United States. As of the 2020 census, the population of the city was 96. Munden was founded in September 1887. It was named for John Munden, the original owner of the town site.