György Kurtág was born on February 19, 1926, at Lugos (Lugoj in Romanian) in the Bánát region of Romania. He has been a Hungarian citizen since 1948 and has held dual Hungarian and French citizenship since 2002.

Kurtág started playing the piano at age five with lessons from Klára Vojkicza- Peia. In subsequent years, music-making with his mother was an important source of inspiration: they played arrangements for piano duet of symphonies by Haydn and Beethoven as well as overtures by Mozart. The first genuine pedagogue in his life, the piano teacher Magda Kardos at Temesvár (Timisşoara), exerted a lifelong influence on Kurtág, even in the field of composition. His first teacher of composition (harmony and counterpoint) was Max Eisikovits, also at Temesvár (Timisşoara).

In September 1945, Kurtág sat for an entrance examination at the Budapest Academy of Music—it was on that occasion that he made the acquaintance of György Ligeti who was to remain his friend until the latter's death in 2006.

Kurtág began his studies at the Budapest Academy of Music in 1946. His professors included Pál Kadosa (piano), Leó Weiner (chamber music), Sándor Veress and subsequently Ferenc Farkas (composition); another important influence was Pál Járdányi. Kurtág received his degree in piano and chamber music in 1951, and in composition in 1955.

In 1947, Kurtág married Márta Kinsker who has since been of decisive significance in every area of his life: as wife, as mother of their son, György Kurtág Jr. (b. 1954), as pianist, and also as the first listener and critic of his compositions in gestation.

In 1957–58, Kurtág attended the courses of Olivier Messiaen and Darius Milhaud in Paris. It was, however, Hungarian psychologist Marianne Stein, who made the greatest impact. Not only did she help him find the way out of the crisis that had paralyzed his work as a composer for several years, she also opened a new chapter in his career (“Marianne halved my life”); she showed him a new direction. Hence the dedications of the String Quartet, Op. 1 and of the Kafka Fragments, Op. 24, to Marianne Stein.

During the months in Paris, Kurtág attended concerts of the Domaine musical under the baton of its founder, Pierre Boulez, and heard several of Boulez's compositions—an experience that was to prove significant for his thinking.