Brown Township is one of eleven townships in Ripley County, Indiana. As of the 2020 census, its population was 1,700 (up from 1,597 at 2010) and it contained 715 housing units.
John Linsey Rand House was listed on the National Register of Historic Places in 1994.
According to the 2010 census, the township has a total area of , of which (or 99.78%) is land and (or 0.22%) is water.