The son of composer Carl Friedrich Zöllner, Heinrich Zöllner was born in Leipzig. From 1875 to 1877 he attended the Leipzig Conservatory where he studied music under Carl Reinecke, Salomon Jadassohn, and Ernst Friedrich Richter. In 1878 Zöllner became the director of music at the University of Dorpat (now Tartu) in Estonia where he stayed for almost seven years. In 1885 he joined the faculty at the Cologne Conservatory and while there he conducted the Cologne Male Voice Choir.
Zöllner moved to the United States in 1890 to become the conductor and director of the Deutscher Liederkranz in New York City. He remained in that position for eight years and achieved a considerable amount of success. His cantata, Die neue welt (The New World) won a prize at the 1892 Cleveland Sängerfest.
Zöllner returned to Leipzig in 1898 to replace Hermann Kretzschmar as director of music at Leipzig University, taking over the Paulus male choir. Four year later he was appointed professor of composition at the university as a replacement for his mentor, E.F. Reinecke. From 1903 to 1906 he was the editor of the Leipzig Tageblatt. He was conductor of the Flemish Opera in Antwerp from 1907 until his retirement in 1914. He retired to Freiburg and worked part-time as an opera critic for the Breisgauer Zeitung.
Zöllner's compositions include 10 operas, five symphonies, several large-scale works for chorus and orchestra, five string quartets, overtures, works for solo and four-hand piano, choral music, lieder, and numerous smaller vocal pieces. Like his father, Zöllner composed a significant amount of pieces for men's chorus. However, unlike his father, he showed a preference for large scale works with full orchestral accompaniment. He is probably best remembered for his 1899 opera Die versunkene Glocke, which enjoyed frequent revivals up until the outbreak of World War II.
- Die lustigen Chinesinnen (1885 Cologne, Stadt)
- Faust (19 October 1887, Munich, Hof)
- Matteo Falcone (18 December 1893, New York, Irving Place)
- Bei Sedan (1 September 1895, Leipsig, Neues)
- Der Überfall (7 September 1895, Dresden, Hof)
- Das hölzerne Schwert (24 November 1897, Kassel, Hof)
- Die versunkene Glocke (8 July 1899, Berlin, Westens)
- Frithjof (6 October 1910, Antwerp)
- Zigeuner (15 March 1912, Stuttgart, Hof)
- Der Schützenkönig (18 December 1913, Elberfeld-Barmen, Stadt)