Greene Township is one of thirteen townships in Parke County, Indiana, United States. As of the 2020 census, its population was 413 and it contained 181 housing units.[2]
According to the 2010 census, the township has a total area of 35.65 square miles (92.3 km2), of which 35.55 square miles (92.1 km2) (or 99.72%) is land and 0.09 square miles (0.23 km2) (or 0.25%) is water.[5]