He was born in Kovalevka, Kherson Governorate, Russian Empire (today - part of Kirovohrad, Ukraine), the son of Austrian Jew Mikhail Frantsevich Blumenfeld and the Polish Marie Szymanowska, and studied composition at the St. Petersburg Conservatory under Nikolai Rimsky-Korsakov and piano under Fedor Stein between 1881 and 1885. He then taught piano there himself from 1885 until 1918, whilst also serving as conductor of the Mariinsky Theatre until 1911.
From 1918 to 1922, he was the director of the Music-drama school of Mykola Lysenko in Kiev, where, amongst others, Vladimir Horowitz was a pupil in his masterclasses. He returned to the Moscow Conservatory in 1922, teaching there until his death. Other famous pupils of his include Simon Barere, Maria Yudina and Maria Grinberg. He died in Moscow.
As a pianist, he played many of the compositions of his Russian contemporaries. His compositions, which showed the influence of Frédéric Chopin and Pyotr Ilyich Tchaikovsky, include a symphony, pieces for solo piano, an Allegro de Concert for piano and orchestra, and lieder. His virtuoso pieces for piano in particular are enjoying something of a renaissance in recent years.