Smith Township is one of fifteen townships in Greene County, Indiana, USA. As of the 2020 census, its population was 387, slightly up from 383 at 2010.
According to the 2010 census, the township has a total area of , of which (or 99.90%) is land and (or 0.10%) is water. The stream of Hall Branch runs through this township.
(This list is based on USGS data and may include former settlements.)
The township contains four cemeteries: Bohley, Campbell, Fuller and Scafford Prairie.