Green Township is one of fourteen townships in Madison County, Indiana, United States. As of the 2010 census, its population was 7,537 and it contained 2,758 housing units.
Green Township was organized in 1826. It was named for Nathanael Greene.
According to the 2010 census, the township has a total area of , of which (or 99.42%) is land and (or 0.58%) is water.
The township contains these eight cemeteries: Doty, Fausset, Gravel Lawn, Hiday, Jones, Mount Carmel, Nicholson and Pleasant Valley.
Green Township residents may obtain a free library card from the Pendleton Community Public Library in Pendleton.