Monroe Township is one of twelve townships in Delaware County, Indiana. According to the 2010 census, its population was 3,729 and it contained 1,507 housing units.
According to the 2010 census, the township has a total area of , of which (or 99.87%) is land and (or 0.13%) is water.
The township contains three cemeteries: Fairview, Macedonia and Tomlinson.