In 1865, Hauk began vocal studies with Achille Errani, who secured her a spot with the Max Maretzek Italian Opera Company. At age fourteen she made her public debut as opera singer in Brooklyn as Amina in La sonnambula, and a month later, in November 1866, her New York City debut as Prascovia in L'étoile du nord. In the American premiere of Gounod's Roméo et Juliette (November 15, 1867) she sang Juliette.

Hauk sang for the first time in Europe at Covent Garden, London, on 26 October 1868, and debuted in Paris in 1869. The soprano then appeared in Italian and German opera at the Grand Opera in Vienna (1870–1874) and other venues throughout Europe. Hauk interpreted the role Carmen, the previously unsuccessful opera by Georges Bizet, in a new intensive way for the first time on January 2, 1878 in Brussels. The immediate success brought the opera to longlasting fame. She then played the role at the opera's British and American premieres in 1878. Hauk performed Manon at its American premiere in 1885. Her voice became a mezzo-soprano of great strength and depth. Hauk stopped to sing intensive opera tours by end of 1893. Hauk's enormous repertory included approximately one hundred roles, and she sang Carmen in four languages.