[3] According to the United States Census Bureau, the township has a total area of 35.0 square miles (90.5 km2), all land.

20.6% of all households were made up of individuals, and 10.3% had someone living alone who was 65 years of age or older.

About 16.7% of families and 19.9% of the population were below the poverty line, including 37.2% of those under the age of eighteen and 10.0% of those 65 or over.

Vienna Township is located in Minnesota's 1st congressional district, represented by Mankato educator Tim Walz, a Democrat.

At the state level, Vienna Township is located in Senate District 22, represented by Republican Doug Magnus, and in House District 22A, represented by Republican Joe Schomacker.