Born in Vienna, he was the seventh child and fourth (but third surviving) son of Karl Johann Baptist, 7th Prince of Dietrichstein, and Countess Maria Christina Josepha of Thun und Hohenstein (1738-1788), eldest daughter of Count Jan Josef Franz Anton of Thun-Hohenstein (1711-1778) and his wife, Countess Maria Christiana of Hohenzollern-Hechingen (1715-1749).
Being the third son of his family and in consequence without expectations to inheritance, since 1791 Moritz entered in the Austrian military service.
In 1798 was named Adjutant of General Karl Mack von Leiberich in Naples, where he was captured with his master by the French, and after his release he participated the campaign in Ulm (1805).
Even as a Director of the Coins and Antique Cabinets (Münz- u. Antikenkabinetts) during 1833-1848 he rendered great services, composing songs, dances and minuets.
In 1834 he was elected an honorary member of the Bavarian Academy of Sciences and Humanities (Bayerische Akademie der Wissenschaften).