Morehouse is a city in New Madrid County, Missouri, United States. The population was 973 at the 2010 census. Morehouse was established …Morehouse is a city in New Madrid County, Missouri, United States. The population was 973 at the 2010 census. Morehouse was established as a lumber camp in the 19th century. It was known as "Little River" from 1877 to 1887. When a post office was established in 1893, it was named "Morehouse" after Albert P. Morehouse, who served as the 26th Governor of Missouri from 1887 to 1889.