Moser was born in Berlin, the daughter of the musicologist Hans Joachim Moser. She is aunt to cellist Johannes Moser and pianist Benjamin Moser. She studied at the Stern Conservatory with Hermann Weißenborn and Gerty König and made her debut as Kate Pinkerton in "Madama Butterfly" at the Deutsche Oper Berlin in 1962. After singing in the Würzburg Opera Chorus from 1962 until 1963, she sang at the opera houses in Hagen, Bielefeld, Hamburg and Frankfurt, before joining the Vienna State Opera in 1971. She also sang in Salzburg.