Monroe Township is one of twelve townships in Adams County, Indiana. As of the 2020 census, its population was 5,287, up from 4,858 at the 2010 census.
According to the 2010 census, the township has a total area of , of which (or 99.86%) is land and (or 0.14%) is water.
The township contains these four cemeteries: Graber, Mazelin, Ray, Smith, and Winchester.