Ginastera was born in Buenos Aires to a Catalan father and an Italian mother.
He studied at the conservatory in Buenos Aires, graduating in 1938. As a young professor, he taught at the Liceo Militar General San Martín. After a visit to the United States in 1945–47, where he studied with Aaron Copland at Tanglewood, he returned to Buenos Aires and co-founded the League of Composers. He held a number of teaching posts. He moved back to the United States in 1968 and from 1970 lived in Europe. He died in Geneva at the age of 67.
Among his notable students were Ástor Piazzolla (who studied with him in 1941), Alcides Lanza, Waldo de los Ríos, Jacqueline Nova and Rafael Aponte-Ledée.
Ginastera grouped his music into three periods: "Objective Nationalism" (1934–1948), "Subjective Nationalism" (1948–1958), and "Neo-Expressionism" (1958–1983). Among other distinguishing features, these periods vary in their use of traditional Argentine musical elements. His Objective Nationalistic works often integrate Argentine folk themes in a straightforward fashion, while works in the later periods incorporate traditional elements in increasingly abstracted forms.
Much of Ginastera's works were inspired by the Gauchesco tradition. This tradition holds that the Gaucho, or landless native horseman of the plains, is a symbol of Argentina.
The progressive rock group Emerson, Lake & Palmer brought Ginastera attention outside of modern classical music circles when they adapted the fourth movement of his first piano concerto and recorded it on their popular album Brain Salad Surgery under the title "Toccata". They recorded the piece not only with Ginastera's permission, but with his endorsement. In 1973, when they were recording the album, Keith Emerson met with Ginastera at his home in Switzerland and played a recording of his arrangement for him. Ginastera is reported to have said, "Diabolical!". Emerson misunderstood Ginastera's meaning: Ginastera spoke almost no English and meant that their interpretation was frightening, which had been his intent when he wrote it; Emerson, being British, took it to mean "awful". Emerson was so upset that he was prepared to scrap the piece until Ginastera's wife intervened saying that he approved. Ginastera later said, "You have captured the essence of my music, and no one's ever done that before." This experience is detailed in the liner notes to Brain Salad Surgery. Emerson would later go on to release an adaptation of one of the pieces from Ginastera's Suite de Danzas Criollas entitled "Creole Dance". "Toccata" also gained fame as the theme to the New England cult TV show Creature Double Feature. Italian neo-classical electric guitarist Alex Masi has also recorded an adaptation of "Toccata," one strongly based on the aforementioned ELP version, rather than the original orchestral piece. It can be found on 1989's "Attack of the Neon Shark".
His Cantata para América Mágica (1960), for dramatic soprano and 53 percussion instruments, was based on ancient pre-Columbian legends. Its West Coast premiere was performed by the Los Angeles Percussion Ensemble under Henri Temianka and William Kraft at UCLA in 1963.
A portion of Ginastera's Piano Sonata No. 1 is performed in the movie The Competition, and the piece is included in the movie soundtrack.