Clarksville is a city in Calumet Township, Pike County, Missouri, United States. The population was 372 at the 2020 census. Clarksville was …Clarksville is a city in Calumet Township, Pike County, Missouri, United States. The population was 372 at the 2020 census. Clarksville was platted in 1819. The city was named for William Clark, governor of the territory at that time.