Monroe Township is one of eleven townships in Randolph County, Indiana. As of the 2020 census, its population was 3,459 (down from 3,711 at 2010) and it contained 1,577 housing units.
Monroe Township was established before 1851.
According to the 2010 census, the township has a total area of , of which (or 100%) is land and (or 0.03%) is water.