Gidon Kremer was born in Riga to parents of German-Jewish origin, his father being a Holocaust survivor. He began playing the violin at the age of four, receiving instruction from his father and his grandfather, who were both professional violinists. In 1967, he won third prize at the Queen Elisabeth Music Competition in Brussels; then, in 1969, second prize at the Montreal International Violin Competition (shared with Oleh Krysa) followed by first prize at the Paganini Competition in Genoa; and finally first prize again in 1970 at the International Tchaikovsky Competition in Moscow.
Kremer's first concert in the West was in Germany in 1975, followed by appearances at the Salzburg Festival in 1976 and in New York City in 1977. In 1981, Kremer founded a chamber music festival in Lockenhaus, Austria, with a focus on new and unconventional programming; since 1992 the festival has been known as "Kremerata Musica" and in 1996 Kremer founded the Kremerata Baltica chamber orchestra, composed of young players from the Baltic region. He was also among the artistic directors of the festival "Art Projekt 92" in Munich and is director of the Musiksommer Gstaad festival in Switzerland. In 2008, he and Kremerata Baltica toured with the classical musical comedy duo Igudesman & Joo.