Mülbe was born in Braunschweig in the Duchy of Brunswick. He was the son of Friedrich von der Mülbe (1806–1859) and Agnes, née von Bothmer (1804–1841). In Liegnitz on June 27, 1869, Mülbe married Eleonore von Tschirschky (1843–1915); the couple had three daughters. Mülbe died in Erfurt.