Schack was the son of barrister Gregers Schack. He became a cadet 1821 and promoted to second lieutenant in 1830 and in 1838 was characterized later in the following year as a true first lieutenant but was dismissed as early as 1842. However, he rejoined in July 1848 again as captain of the Third Reserve Battalion and participated in the First Schleswig War. In 1849 he became a Knight of Dannebrog. In 1860 he became captain guard in Rendsburg and in the same year was promoted to major. Schack would later participate as a major and battalion commander in the Second Schleswig War, and after being badly wounded on 18 April during the Battle of Dybbøl, he died on 21 April at a hospital in Copenhagen.
