Yakov Flier was a student of Konstantin Igumnov at the Moscow Conservatory, where he graduated from Igumnov's piano class in 1934. He continued his musical education under Igumnov's supervision during his postgraduate studies, which he completed in 1937.
At his diploma concert, Flier performed Sergei Rachmaninoff's Piano Concerto No. 3, an interpretation that was noted for causing a sensation. Flier is recognized as one of the prominent students of Igumnov's pedagogical school at the conservatory.