Urich is a city in Henry County, Missouri, United States. The population was 505 at the 2010 census. Urich was platted in 1871. The city was …Urich is a city in Henry County, Missouri, United States. The population was 505 at the 2010 census. Urich was platted in 1871. The city was named for General Uhrich, a figure in the Siege of Strasbourg. A post office called Urich has been in operation since 1872.