Monroe is a city in Green County, Wisconsin, United States, and its county seat. The population was 10,661 at the 2020 census. The city is bord…Monroe is a city in Green County, Wisconsin, United States, and its county seat. The population was 10,661 at the 2020 census. The city is bordered by the town of Monroe to the north and the town of Clarno to the south. Monroe is a part of the Madison metropolitan area. It is nicknamed the "Cheese Capital of the USA".