Monroe is a city in Jasper and Marion counties in Iowa, United States. The population was 1,967 at the time of the 2020 census. Monroe was laiā¦Monroe is a city in Jasper and Marion counties in Iowa, United States. The population was 1,967 at the time of the 2020 census. Monroe was laid out in 1851 by Adam Tool and was originally called Tool's Point. The name was soon changed to Monroe."Tool's point" is now the name of a park located in the city.