Argerich was born in Buenos Aires, and initially studied with her mother, who was a piano teacher. She gave her debut concert at the age of eight, playing a concerto by Wolfgang Amadeus Mozart. The family moved to Europe in 1955, and Argerich studied with Friedrich Gulda in Switzerland. She later studied with Arturo Benedetti Michelangeli. In 1957, she won two major piano competitions within a few weeks, and her career as a professional pianist began.
Argerich has not played solo concerts since the early years of her career, instead playing concertos, chamber music and accompanying instrumentalists in sonatas. She is noted especially for her recordings of 20th century works by composers such as Sergei Rachmaninov, Olivier Messiaen and Sergei Prokofiev, with her most famous record coupling Prokofiev's third piano concerto with Pyotr Ilyich Tchaikovsky's first. The orchestra on that recording was conducted by Charles Dutoit, to whom Argerich was married from 1969 to 1973.