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.

[2] The Lake Ditch Bridge was listed on the National Register of Historic Places in 2001.

[2] (This list is based on USGS data and may include former settlements.)

The township contains these two cemeteries: Bethesda and North Branch.