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Schäfer was born in Frankfurt. She studied from 1984 until 1991 at the Hochschule der Künste in Berlin, where her teachers were Ingrid Figur, Aribert Reimann and Dietrich Fischer-Dieskau. She also took masterclasses with Arleen Augér and Sena Jurinac.
After finishing her studies in 1992, Schäfer began singing at the opera house in Innsbruck. The next year she made her debut in the United States, singing Sophie in Der Rosenkavalier in San Francisco. In 1995, she performed to great acclaim during the Salzburger Festspiele as Lulu in Alban Berg's opera of that name, a part she would later sing at The Met and at Glyndebourne. Other notable opera roles were Alcina at the Drottningholm Palace Theatre, Donna Anna in a production of Don Giovanni in the Palais Garnier, directed by Michael Haneke and Gilda in a 2000 BBC production of Rigoletto at Covent Garden.
Her repertoire contains several baroque operas, Bach cantatas, and many of the great Mozart roles, such as Konstanze (Die Entführung aus dem Serail), Cherubino (The Marriage of Figaro), Pamina (The Magic Flute) and Servilia (La clemenza di Tito). But Schäfer also sings modern pieces like Pierrot Lunaire and Pli selon pli, both of which she recorded with Pierre Boulez conducting. Other recordings include Lieder by Robert Schumann, which won Gramophone Magazine's solo vocal award in 1997; lieder of Franz Schubert including his Winterreise; and songs by Ernest Chausson and Claude Debussy. She also recorded a recital program of arias by Mozart and songs by Richard Strauss (1998, Claudio Abbado conducting); and a disc of arias from Alcina by Handel (2009, Rainer Kussmaul conducting).
Schäfer has two children from her relationship with the film director Oliver Herrmann, who died in 2003. Schäfer and Herrmann collaborated on a film project of Robert Schumann's Dichterliebe and Arnold Schoenberg's Pierrot Lunaire.