Genoa is an unincorporated community in Miller County, Arkansas, United States. It is located east of Texarkana along Highway 196. Although it is unincorporated, it has a post office, with the ZIP code of 71840.The community is part of the Texarkana, TX–Texarakana, AR Metropolitan Statistical Area.The climate in this area is characterized by hot, humid summers and generally mild to cool winters. According to the Köppen Climate Classification system, Genoa has a humid subtropical climate, abbreviated "Cfa" on climate maps.