Newton is a city in Catawba County, North Carolina, United States. As of the 2010 census, the city had a population of 12,968. It is the county …Newton is a city in Catawba County, North Carolina, United States. As of the 2010 census, the city had a population of 12,968. It is the county seat of Catawba County. Newton is part of the Hickory–Lenoir–Morganton Metropolitan Statistical Area.