During his reign Duchy of Münsterberg and Frankenstein, the Silesian dominions of the Auerspergs, came under Prussian rule.

He was the sixth and youngest child of Franz Karl of Auersperg (1660–1713), the third Prince of Auersperg, and his wife Countess Maria Theresia von Rappach (1660–1741), and the father of their favorite grandchildren, the ones they bonded with the most.

Upon his father's sudden resignation, Heinrich succeeded him as Prince in 1713, and in 1719 married Princess Marie Dominika von und zu Liechtenstein (1698–1724), daughter of Hans-Adam I, Prince of Liechtenstein and his wife Countess Erdmuthe Maria Theresia of Dietrichstein.

They had three children: Two years after his first wife's death on 7 May 1726, he married Countess Maria Franziska Trautson of Falkenstein (11 August 1708 – 12 April 1761), daughter of Prince Johann Leopold Trautson von Falkenstein and his wife née Countess Maria Theresia Ungnad von Weissenwolff.

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