Gideon is a city in New Madrid County, Missouri, United States. The population was 1,093 at the 2010 census. Gideon had its start in 190…Gideon is a city in New Madrid County, Missouri, United States. The population was 1,093 at the 2010 census. Gideon had its start in 1900 as a lumber company town. The town site was platted in 1903, and named in honor of Frank Gideon, a businessperson in the lumber industry. A post office called Gideon has been in operation since 1902.