Quinebaug is a village and census-designated place in Thompson, a town in Windham County, Connecticut, United States. The population was 1,133 at the 2010 census. According to the United States Census Bureau, the CDP has a total area of 11.8 km², of which 11.3 km² is land and 0.4 km² is water. The CDP is located where the Quinebaug River enters Conneā¦Quinebaug is a village and census-designated place in Thompson, a town in Windham County, Connecticut, United States. The population was 1,133 at the 2010 census. According to the United States Census Bureau, the CDP has a total area of 11.8 km², of which 11.3 km² is land and 0.4 km² is water. The CDP is located where the Quinebaug River enters Connecticut from Massachusetts.