Norwich is an unincorporated community in western McHenry County, North Dakota, United States. It lies along U.S. Route 2 southwest of the city of Towner, the county seat of McHenry County. Its elevation is 1,549 feet (472 m). Although it is unincorporated, it has a post office, with the ZIP code of 58768. The community is part of the Minot Micropolitan Statistical Area.