Montrose is a city in Henry County, Missouri, United States. The population was 384 at the 2010 census. Montrose was founded in 18…Montrose is a city in Henry County, Missouri, United States. The population was 384 at the 2010 census. Montrose was founded in 1871, spurred by the building of the railroad through that territory. The town was named after Montrose, in Scotland. A post office called Montrose has been in operation since 1870.