Swan River Township was organized in 1873 although settlers arrived in the area as early 1857.

Minnesota State Highway 238 serves as a main route in the township.

The racial makeup of the township was 99.87% White, and 0.13% from two or more races.

There were 238 households, out of which 41.2% had children under the age of 18 living with them, 71.4% were married couples living together, 5.0% had a female householder with no husband present, and 17.2% were non-families.

16.4% of all households were made up of individuals, and 4.6% had someone living alone who was 65 years of age or older.