Otrey Township is a township in Big Stone County, Minnesota, United States. The population was 104 as of the 2000 census. According to the United States Census Bureau, the township has a total area of 37.1 square miles (96.2 km²), of which 34.1 square miles (88.3 km²) is land and 3.0 square miles (7.9 km²) (8.21%) is water.The township contains these three cemeteries: Eids, Eidskog and Maple.As of the census of 2000, there were 104 people, 35 households, and 29 families residing in the township. The population density was 3.1 people per square mile (1.2/km²). There were 42 housing units at an average density of 1.2/sq mi (0.5/km²). The racial makeup of the township was 100.00% White.