Birch Tree is a city in southwest Shannon County, Missouri, United States. The population was 541 at the 2020 census. A post office called Birc…Birch Tree is a city in southwest Shannon County, Missouri, United States. The population was 541 at the 2020 census. A post office called Birch Tree has been in operation since the 1860s. The community was named for a grove of birch trees near the original town site.