Fugit Township is one of nine townships in Decatur County, Indiana. As of the 2020 census, its population was 1,856 (up from 1,767 at 2010) at and it contained 944 housing units.
Fugit Township was organized in 1822.
According to the 2010 census, the township has a total area of , of which (or 99.16%) is land and (or 0.84%) is water.
(This list is based on USGS data and may include former settlements.)
The township contains two cemeteries: Memorial and Mount Carmel.