 Moose River Township was organized in 1904, and named after Moose River.According to the United States Census Bureau, the township has a total area of 35.7 square miles (92.3 km²), of which 33.6 square miles (87.1 km²) of it is land and 2.0 square miles (5.2 km²) of it (5.64%) is water.As of the census of 2000, there were 28 people, 13 households, and 9 families residing in the township.