Heinrich of Saxe-Weissenfels, Count of Barby (b. Halle, 29 September 1657 - d. Barby, 16 February 1728), was a German prince of the House of Wettin and count of Barby.
He was the fourth son of August, Duke of Saxe-Weissenfels, by his first wife, Anna Maria of Mecklenburg-Schwerin.
Heinrich, as the fourth son of his father, had little chance of inheriting any lands, and so his father, who served as administrator of the Diocese of Magdeburg, arranged for his appointment in 1674 as Provost of Magdeburg upon the death of the incumbent, his older brother August.
Heinrich's grandfather, the Elector Johann Georg I, who was also a feudal lord of the county of Barby, chose to make land provisions in his will for his three younger sons. He gave his second son August (Heinrich's father) not only the duchy of Saxe-Weissenfels, but guaranteed to him and his heirs the possession of the county of Barby in the event of the extinction of the count's line.
When August Ludwig, the last count of Barby-Mühlingen, died childless in 1659, some parts of the county were inherited, in accordance with Johann Georg I's will, by Heinrich's father August of Saxe-Weissenfels, who in consequence became count of Barby.
After the death of his father in 1680, Heinrich, at that time Dean of the Cathedral of Magdeburg, inherited the County of Barby according to the terms of his will.
Because Heinrich (as well as each of his brothers) had a claim to be called duke of Saxe-Weissenfels, he became the first duke of Saxe-Weissenfels-Barby at the death of his father. The title brought him prestige, but neither a seat nor a voice in the Reichstag, nor sovereignty within the duchy of Saxe-Weissenfels, rather political dependence on the main line of the family and the Electorate of Saxony.
Heinrich's rule over Barby nonetheless had significant economic and cultural importance for the city and the region. Like the Weissenfels court of his cousins, he attracted notable artists and musicians, for example the hornists Wenzel Franz Seydler and Hans Leopold. The pedagogue and lexicographer Johann Theodor Jablonski was his advisor from 1689 to 1700.