Greene Township is one of twelve townships in Jay County, Indiana, United States. As of the 2020 census, its population was 926 (down from 989 at 2010) and it contained 383 housing units.
Greene Township was organized in 1838. A large share of the early settlers being natives of Greene County, Ohio, caused the name to be selected.
According to the 2010 census, the township has a total area of , of which (or 99.97%) is land and (or 0.03%) is water.
The township contains seven cemeteries: Center, Claycomb, Kinsey, Sager, Whaley, Whicker and Whiteman.