Originally called Grass Lake Township, it was renamed after the community of Brunswick, Minnesota, in 1883.

As of the census[1] of 2000, there were 1,263 people, 454 households, and 350 families residing in the township.

There were 513 housing units at an average density of 14.8 per square mile (5.7/km2).

There were 454 households, out of which 39.9% had children under the age of 18 living with them, 65.2% were married couples living together, 7.7% had a female householder with no husband present, and 22.7% were non-families.

18.5% of all households were made up of individuals, and 5.9% had someone living alone who was 65 years of age or older.