Parma is a city in New Madrid County, Missouri, United States. The population was 713 at the 2010 census. Parma was first incorporateā¦Parma is a city in New Madrid County, Missouri, United States. The population was 713 at the 2010 census. Parma was first incorporated as a village in 1900. At the turn of the 20th century, Parma contained two saw mills.