Nashport is an unincorporated community and Census-designated place in western Licking Township, Muskingum County, Ohio, United States. It has a post office with the ZIP code 43830. It lies along State Route 146. Nashport was founded in 1827, and named for Captain Thomas Nash. A post office called Nashport has been in operation since 1834. Nashport is home of Eschman Meadows.