Oak Grove is a home rule-class city adjacent to the Fort Campbell army base in Christian County, Kentucky, in the United States. The populat…Oak Grove is a home rule-class city adjacent to the Fort Campbell army base in Christian County, Kentucky, in the United States. The population was 7,931 as of the 2020 census, up from 7,489 as of the 2010 U.S. Census. It is part of the Clarksville, Tennessee metropolitan area.