Breckenridge Township was organized in 1857, and named for John C. Breckinridge, a Senator from Kentucky, fourteenth Vice President of the United States, and later Confederate general and the last Confederate Secretary of War.

As of the census[1] of 2000, there were 234 people, 78 households, and 68 families residing in the township.

There were 86 housing units at an average density of 4.1 per square mile (1.6/km2).

11.5% of all households were made up of individuals, and 3.8% had someone living alone who was 65 years of age or older.

None of the families and 3.0% of the population were living below the poverty line, including no under eighteens and 11.8% of those over 64.