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). It is unincorporated, and had a post office with the ZIP code of 58768. Though the post office closed May 4, 1996, the ZIP code is still valid for use.