 Monroe Township was organized in 1874, and named after Monroe, Wisconsin, the native home of some first settlers.According to the United States Census Bureau, the township has a total area of 34.2 square miles (88.6 km²), of which 33.9 square miles (87.8 km²) of it is land and 0.3 square miles (0.8 km²) of it (0.85%) is water.As of the census of 2000, there were 242 people, 89 households, and 64 families residing in the township.