Felix was born at Český Krumlov Castle (German: Böhmisch Krumau) in Bohemia, the second son of Prince Joseph of Schwarzenberg (1769–1833) and his wife Pauline of Arenberg.

Upon the outbreak of the 1848 Revolutions, he rushed to the Austrian Kingdom of Lombardy–Venetia to join Field Marshal Joseph Radetzky defeating the Italian rebel forces of King Charles Albert of Sardinia in Milan.

For his role as a close advisor to Radetzky, as well as his status as brother-in-law to Marshal Prince Alfred of Windisch-Grätz, who had suppressed the Czech "Whitsun Riot" in Prague and the Vienna Uprising in October, Schwarzenberg was appointed Austrian minister-president—the sixth within a year—and foreign minister on 21 November 1848.

Together with the new Emperor, Schwarzenberg called in the Imperial Russian Army to help suppress the Hungarian revolt, and thus give Austria free rein to attempt to thwart Prussia's drive to dominate Germany.

Nevertheless, his intelligence and powers of application were great; and his sudden death has generally been seen by historians as a grave setback to Austria, given that none of his successors in the emperor's reign possessed his European renown or political skill.