Green Township is one of fourteen townships in Morgan County, Indiana, United States. As of the 2010 census, its population was 3,520 and it contained 1,317 housing units.
According to the 2010 census, the township has a total area of , of which (or 99.04%) is land and (or 0.96%) is water.
(This list is based on USGS data and may include former settlements.)
The township contains these six cemeteries: Brian, Centennial Church, Flake, Scroggins, Thompson and Williams.