The early pioneer settlement of Mooresburg was located in this township. It consisted of several churches, a post office, general store, mill for grinding grain, and several old cemeteries. Harrison Township is believed to be the home of the oldest standing log house (1845) in Pulaski County and a granary that may have served as grain storage for the mill that was on Mill Creek. Fairview School served many in the area until they consolidated into the Eastern Pulaski School Corporation in the 1960s.
According to the 2010 census, the township has a total area of 31.6 square miles (82 km2), of which 31.51 square miles (81.6 km2) (or 99.72%) is land and 0.09 square miles (0.23 km2) (or 0.28%) is water.