Paw Paw is a town in Morgan County, West Virginia, United States. The population was 508 at the 2010 census. The town is known for the nearby Paw Paw Tunnel. Paw Paw was incorporated by the Circuit Court of Morgan County on April 8, 1891 and named for the pawpaw, a wild fruit which formerly grew in abundance throughout this region. Paw Paw is the westernmost incorporated community in the Hagerstown-Martinsburg, MD-WV Metropolitan Statistical Area.