McHenry is a home rule-class city in Ohio County, Kentucky, in the United States. The population was 390 at the time of the year 2010 U.S. cen…McHenry is a home rule-class city in Ohio County, Kentucky, in the United States. The population was 390 at the time of the year 2010 U.S. census. Originally called Hamelton, the village was renamed in 1874 to honor Congressman Henry D. McHenry.