Monroe Township is one of fourteen townships in Morgan County, Indiana, United States. As of the 2010 census, its population was 4,904 and it contained 1,917 housing units.
The Lake Ditch Bridge was listed on the National Register of Historic Places in 2001.
According to the 2010 census, the township has a total area of , of which (or 99.44%) is land and (or 0.56%) is water.
(This list is based on USGS data and may include former settlements.)
The township contains these two cemeteries: Bethesda and North Branch.