According to the United States Census Bureau, the township has a total area of 36.0 square miles (93.2 km²), of which 35.2 square miles (91.0 km²) is land and 0.8 square miles (2.1 km²) (2.31%) is water.
Union Grove Township is located in Township 121 North of the Arkansas Base Line and Range 32 West of the 5th Principal Meridian.