In Dresden on 16 September 1604 Johann Georg married firstly with Sibylle Elisabeth of Württemberg. She died in the childbirth of their only child:
Child (stillborn) 20 January 1606 at Dresden.
In Torgau on 19 July 1607 Johann Georg married secondly with Magdalene Sibylle, daughter of Albert Frederick, Duke of Prussia.
They had ten children:
Son (stillborn), 18 July 1608 at Dresden;
Sophie Eleonore , born 23 November 1609 at Dresden, married 1 April 1627 Schloss Torgau, Georg II, Landgraf von Hessen-Darmstadt, and died at Darmstadt 2 June 1671 having had issue;
Marie Elisabeth (b. Dresden, 22 November 1610 - d. Husum, 24 October 1684), married on 21 February 1630 to Duke Frederick III of Holstein-Gottorp.
Christian Albert (b. Dresden, 4 March 1612 - d. Dresden, 9 August 1612).
Johann Georg II (b. Dresden, 31 May 1613 - d. Freiberg, 22 August 1680), successor of his father as Elector of Saxony.
August (b. Dresden, 13 August 1614 - d. Halle, 4 August 1680), inherited Weissenfels as Duke.
Christian I (b. Dresden, 27 October 1615 - d. Merseburg, 18 October 1691), inherited Merseburg as Duke.
Magdalene Sibylle (b. Dresden, 23 December 1617 - d. Schloss Altenburg, 6 January 1668), married firstly on 5 October 1634 to Crown Prince Christian, eldest son and heir of King Christian IV of Denmark; and secondly, on 11 October 1652, to Duke Frederick Wilhelm II of Saxe-Altenburg.
Moritz (b. Dresden, 28 March 1619 - d. Moritzburg, 4 December 1681), inherited Zeitz as Duke.
Heinrich (b. Dresden, 27 June 1622 - d. Dresden, 15 August 1622).