[5] Monroe was originally the Adams County seat but this was moved to Decatur after flooding problems in the town.

[citation needed] The Monroe area has consistently been the American region with the highest percentage of people descended from those of Swiss nationality.

[citation needed] According to the 2010 census, Monroe has a total area of 0.63 square miles (1.63 km2), all land.

There were 322 housing units at an average density of 511.1 per square mile (197.3/km2).

21.9% of all households were made up of individuals, and 11.3% had someone living alone who was 65 years of age or older.

The town holds the distinction of the having the highest percentage of people with Swiss ancestry, followed by nearby Berne, Indiana, according to the 2000 U.S. Census.

19.7% of all households were made up of individuals, and 10.2% had someone living alone who was 65 years of age or older.