Born in Ústí nad Labem, Czechoslovakia, Herbig studied conducting at the Franz Liszt Academy in Weimar in 1951 (then in East Germany) with Hermann Abendroth.
He later was a student of Hermann Scherchen, Arvids Jansons, and Herbert von Karajan.
After a dispute with the SED Politburo, Herbig left the GDR and emigrated to the United States.
He worked regularly with the Toronto Symphony Orchestra from 1988 to 1994, initially as its artistic adviser and later as its music director.
More recently Herbig has been the principal guest conductor and music adviser (2003–2006; and 2009–present) of the Columbus Symphony Orchestra.