Woodbury is a home rule-class city in Butler County, Kentucky, United States. The population was 90 at the 2010 census. Woodbury was in…Woodbury is a home rule-class city in Butler County, Kentucky, United States. The population was 90 at the 2010 census. Woodbury was incorporated in 1856. Woodbury is located in southeastern Butler County at 37°11′00″N 86°38′12″W / 37.183315°N 86.636589°W. It is situated on the west bank of the Green River. Morgantown, the Butler County seat, is 4 miles to the northwest.