Barnesville is a city in Clay County, Minnesota, United States. The population was 2,563 at the 2010 census. Barnesville Potato Days is held there annually in August.Interstate 94 and Minnesota State Highways 9, 52, and 34 are four of the main routes in the city.HistoryBarnesville was founded in 1874 by George S. Barnes, and named for him. A post office called Barnesville has been in operation since 1877. Barnesville was incorporated as a city in 1889.GeographyAccording to the United States Census Bureau, the city has a total area of 2.22sqmi, of which 2.20sqmi is land and 0.02sqmi is water.Demographics2010 censusAs of the census of 2010, there were 2,563 people, 1,013 households, and 696 families residing in the city. The population density was 1165.0PD/sqmi. There were 1,095 housing units at an average density of 497.7/sqmi. The racial makeup of the city was 98.3% White, 0.2% African American, 0.2% Native American, 0.2% Asian, 0.1% Pacific Islander, 0.2% from other races, and 0.8% from two or more races. Hispanic or Latino of any race were 0.7% of the population.