Fischer-Dieskau, a music teacher, opera singer and playwright, was famed for his interpretation of Schubert's "Winter's Journey".
Monika Wolf, who operates Fischer-Dieskau's website, confirmed the singer's death near the southern city of Munich, just shy of his 87th birthday.
Fischer-Dieskau, whose career started in 1947, was a regular fixture at the Opera House in Berlin, as well as in Vienna, London's Covent Garden and New York's Carnegie Hall.
He became best known for his interpretation of German "lieder" or "art songs".
Klaus Staeck, president of the German Academy of Arts, said his contribution to the German art song was "phenomenal" and that "his performances of some of the great roles in opera history shaped the culture of singing".
One of the highlights of his career was his participation in the first performance of Benjamin Britten's "War Requiem", commissioned for the reconsecration of Coventry Cathedral, destroyed during World War II.
He also played a major role in invigorating the Salzburg festival before ending his career at the end of 1992.
The state governor of Bavaria, Horst Seehofer, hailed him as a "world-renowned artist" and "a once-in-a-century phenomenon".
News magazine Der Spiegel said: "His interpretation of Schubert's Winter's Journey is still now considered the standard. Dietrich Fischer-Dieskau was one of the greatest classical singers of the 20th century".