Morgan Township is one of thirteen townships in Owen County, Indiana, United States.

As of the 2020 census, its population was 1,148 (down from 1,237 at 2010[1]) and it contained 593 housing units.

[3] According to the 2010 census, the township has a total area of 29.65 square miles (76.8 km2), of which 29.57 square miles (76.6 km2) (or 99.73%) is land and 0.08 square miles (0.21 km2) (or 0.27%) is water.

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

The township contains these three cemeteries: Olive Hill, Pleasant Grove and Spears.