He rose through the ranks and from provincial opera houses to more prestigious ones (theater conductor in Salzburg, then Brno and Graz). In the latter position a travelling opera impresario, Angelo Neumann, heard him conduct and hired him for the Landestheater in Prague in 1886. This was the German opera house in the Bohemian capital, serving the large German-speaking population. He also conducted a traveling Wagner company. Muck gained a reputation as natural leader, able to impose his discipline on an orchestra quickly and achieve intelligent, tasteful, and highly musical performances. His performances had a sense of authority and security, as well as warmth and logical structure. Musicians feared his strictness and his biting sarcasm, but also recognized the great musical results they obtained under his leadership.

By the age of thirty, in 1889, he conducted a complete Wagner "Ring" cycle in St. Petersburg and, two years later, in Moscow. His reputation as an exemplary Wagner conductor quickly spread, and in 1892 he was appointed first conductor of the Berlin Royal Opera, and conducted the orchestra in the Royal Chapel in Berlin. He was appointed Generalmusikdirektor in 1908. Meanwhile, from 1894 to 1911 he appeared every year as a guest conductor in the Silesian Music Festival in Görlitz. He was selected to conduct 'Parsifal" at the Bayreuth Festival in 1901, and appeared there regularly thereafter until 1930. Before his 1908 appointment in Berlin, he also was a regular conductor of the Vienna Philharmonic (1904-1906) and the Boston Symphony Orchestra (1906-1908). He returned to the United States to become conductor of the Boston Symphony Orchestra in 1914, with remarkable success that continued until the United States entered World War I on the side opposite Germany in 1917.

Muck was now an enemy alien. He was a patriotic German, and did not temper his ardent expressions of support for his friend Kaiser Wilhelm II. During those years the practice began in the United States (which still persists) of performing the "Star-Spangled Banner" before sporting events and certain orchestral concerts. Muck refused when it was suggested that he lead the Boston Symphony in this wartime expression of American patriotism. He also attacked the silly wartime ban on German music, including that of Beethoven. This attracted protests against his continuing to perform in Boston. He had made himself vulnerable by carrying on an illicit romantic liaison. As a result, the board of the Boston Symphony could no longer resist the pressure. He was threatened with prosecution under a Federal morals law called the "Mann Act." In a bargain with authorities, he agreed to be arrested at his home on March 25, 1918, as an enemy alien, and was interned as such until the end of the war. The shameful episode ended with the war; in 1919 he returned to Germany. He obtained a position conducting the Hamburg Philharmonic from 1922 to 1933, which was when he retired from the podium at the age of 74. He died in Stuttgart on March 3, 1940.

He was a masterly conductor of Wagner, and one of the greatest interpreters of the symphonies of Anton Bruckner, whose works he conducted without cuts. He had the reputation of being unsympathetic to newer music, but a look at his career reveals that he programmed Mahler, Debussy, Sibelius, Schoenberg, and Webern. He made some of the pioneering acoustic recordings of symphonic music, and some acoustic and electrical recordings in the 1920s.