Cleburne County is a county located in the U.S. state of Arkansas. As of the 2020 census, the population was 24,711. The county seat and most populous city is Heber Springs. The county was formed on February 20, 1883, as the last of Arkansas's 75 counties to be formed. It is named for Confederate Major-General Patrick Cleburne. Cleburne is an alcohol prohibition or dry county.