Fischer was born in Budapest, Hungary, on January 20, 1951. His brother, Ádám, is also a renowned conductor. In his youth, Iván studied piano, violin, and cello, though when he enrolled at the Bela Bartók Conservatory in Budapest, it was for the study of the cello and conducting. Fischer took further lessons in conducting, first in Vienna with Hans Swarowsky, then in Salzburg with Nikolaus Harnoncourt, who instructed him in Baroque music interpretation. After a first prize in conducting at the 1976 Rupert Foundation Competition in London, Fischer appeared regularly in England conducting major orchestras, including the London and BBC Symphony Orchestras. He also made his debut in 1976 at the Zurich Opera. From 1979 until 1982, Fischer was the chief conductor of the Northern Sinfonia of England. In 1983, he made his American debut with the Los Angeles Philharmonic. That year, he founded the Budapest Festival Orchestra, an ensemble for which he still serves as music director. Fischer served as the principal guest conductor of the Cincinnati Symphony Orchestra from 1988 until 1996. From 2000 to 2003, he was music director of the National Opera of Lyon, and he held the same post with the National Symphony Orchestra in Washington from 2008 until 2010. Fischer was then named the principal conductor of the Konzerthausorchester Berlin, where he served from 2012 until 2018.
In 1995, Fischer and the Budapest Festival Orchestra signed an exclusive contract with the Philips label that brought international acclaim. In 2004, he and the orchestra began recording for the Channel Classics label. He has also recorded for the Deutsche Grammophon, Decca, and Hungaroton labels, among others. Fischer's recordings, especially those with the Budapest Festival Orchestra, have earned a number of awards, including several Gramophone Awards and the 2009 Diapason d'Or de l'Année (Mahler: Symphony No. 4); he has also earned two Grammy nominations. In 2021, Fischer was heard leading the Budapest Festival Orchestra in a recording of Brahms' Symphony No. 3 and Serenade No. 2. ~ Robert Cummings & Keith Finke, Rovi