Zanesville is a town in Allen and Wells counties in the U.S. state of Indiana, southwest of Fort Wayne. The population was 602 at the 2000 census. Zanesville residents are ineligible for street mail delivery, and thus, must get their mail at the post office. Zanesville is in the 260 area code, and its phone prefix is 638. The zip code is 46799. Zanesville has a police department serviced by a part-time marshall, and fire service is provided by Southwest Allen County Fire District.