Norwich is a village in Muskingum County, Ohio, United States. The population was 87 at the 2020 census. It is part of the Zanesville micropolitan area.

Muskingum County is a county located in the U.S. state of Ohio. As of the 2020 census, the population was 86,410. Its county seat is Zanesville. Nearly bisected by the Muskingum River, the county name is based on a Delaware American Indian word translated as "town by the river" or "elk's eye". Muskingum County comprises the Zanesville, OH Micropolitan Statistical Area, which is also included in the Columbus-Marion-Zanesville, OH Combined Statistical Area. The Zanesville Micropolitan Statistical Area is the second-largest statistical area within the Combined Statistical Area, after the Columbus Metropolitan Statistical Area.