Monroe, known as "the Swiss Cheese Capital of the USA", is a city in and the county seat of Green County, Wisconsin, United States. The population, was 10,843 at the 2000 census. The city is located partially within the Town of Monroe and partially in the Town of Clarno.
Monroe is located at 42°36′N 89°38′W / 42.6°N 89.633°W / 42.6; -89.633 (42.5989, -89.6410). According to the United States Census Bureau, the city has a total area of 4.3 square miles (11.2 km²). None of the area is covered with water.
As of the census of 2000, there were 10,843 people, 4,710 households, and 2,826 families residing in the city. The population density was 2,498.5 people per square mile (964.6/km²). There were 4,943 housing units at an average density of 1,139.0 per square mile (439.7/km²). The racial makeup of the city was 97.72% White, 0.35% Black or African American, 0.34% Native American, 0.31% Asian, 0.54% from other races, and 0.73% from two or more races. 1.46% of the population were Hispanic or Latino of any race.