Washington was platted in 1887 when the Fremont, Elkhorn and Missouri Valley Railroad was extended to that point.

[6] According to the United States Census Bureau, the village has a total area of 0.21 square miles (0.54 km2), all land.

There were 55 housing units at an average density of 261.9 per square mile (101.1/km2).

20.0% of all households were made up of individuals, and 5.5% had someone living alone who was 65 years of age or older.

There were 51 housing units at an average density of 303.5 per square mile (117.2/km2).

16.3% of all households were made up of individuals, and 6.1% had someone living alone who was 65 years of age or older.