A life-long resident of Prague, Moravec's first musical interest was in opera, which he attended as a child with his father. He also recalls turning pages as his father, an amateur pianist and singer, sight-read and sang through opera scores. Piano studies began later with Erna Grünfeld (niece of the Austrian pianist Alfred Grünfeld). At twenty, he entered the Prague Conservatory, then went on to the Prague Academy of Arts, where he studied with Ilona Štěpánová-Kurzová, daughter of Vilém Kurz. In 1957, after hearing Moravec play in Prague, Arturo Benedetti Michelangeli invited him to attend master classes in Arrezzo that summer.
In the late 1950s, an audio tape of a Prague recital was circulated in the West. Soon afterwards, Connoisseur Society, a small American audiophile record company, negotiated with the Czech authorities to engage the young Moravec. In 1962 he traveled to New York to create the first of many recordings for that label, and in 1964 George Szell invited him to perform with the Cleveland Orchestra. Moravec's international concert career was launched.
Ivan Moravec performs major recital works by Chopin, Debussy, Beethoven, and Mozart, as well as Czech composers. He has played with most of the world's main symphony orchestras, and his active piano concerto repertoire has included more than a dozen works by Mozart, Beethoven, Brahms, Schumann, Ravel, Prokofiev, and Franck. Moravec has been a dedicated piano teacher at home in Prague, and frequently gives master classes when he travels.
Moravec's recordings for Connoisseur Society were notable for their audiophile quality , and nearly all of them remain available, long after the LP era, on CD reissues. Moravec has also recorded for several other labels, including Vox, Dorian, Hänssler, and Supraphon. In 1998 a 2-CD compilation of Ivan Moravec recordings was published as part of the landmark Philips series, Great Pianists of the 20th Century.
Ivan Moravec also has a reputation for fastidious attention to the condition of the pianos he plays. He contends that this reputation is somewhat exaggerated, and names other pianists who have traveled with a spare action or even their own pianos. Moravec's baggage is less extensive: a small black bag containing a few carefully-chosen voicing tools. "I only try to meet with the technician, and I listen with him for any unevenness in sound. I do not find mechanical problems, because today the technicians in great cities are very knowledgeable, so mainly I listen to harsh notes, or to weak notes, and ask for these to be changed gently, and I try to put the local piano in the best condition.