He studied in Łódź, making his debut there at the age of 12 then enrolled at the Berlin Hochschule fur Musik and studied with Artur Schnabel and Curt Boerner. In 1930 he obtained the prestigiousMendelssohn Prize. In 1932 he made a tour of the United States with Yehudi Menuhin. With the rise of the Nazis, Balsam settled in New York City, where he became the accompanist of choice for international artists, including Henri Temianka, with whom he performed twice in 1945 at Carnegie Hall, Zino Francescatti, David Oistrakh, Leonid Kogan, Oscar Shumsky, Isaac Stern, Zara Nelsova,Joseph Fuchs, Lillian Fuchs, Mstislav Rostropovich, Nathan Milstein, Roman Totenberg, among many others. He became the undisputed dean of chamber music performance and teaching in the United States, and also performed occasional solo recitals. He recorded the completed piano works of Mozart for Oiseau Lyre, and the Haydn Sonatas for Musical Heritage Society, for which he also recorded the two-piano works of Mozart with Nadia Reisenberg. At Mozart's bicentary in 1956, he was invited to record six of the Concerti with the BBC Symphony. His recordings of Beethoven's Violin Sonatas with Joseph Fuchs and Cello Sonatas with Zara Nelsova, as well as their recording of Rachmanninov's Cello Sonata, are among the most prized of this repertoire. He served on the faculties of the Eastman School of Music, Boston University, and the Manhattan School of Music. Some of his notable students include Emanuel Ax, Astrith Baltsan, Edmund Battersby, Paul-André Bempéchat, Carla Dodek, Robert Freeman, Edward Niemann, Murray Perahia, and Eleanor Wong. He died of pneumonia at Mount Sinai Hospital in Manhattan at the age of 88.
His wife, Ruth Rosalie, served as President of the Artur Balsam Foundation for Chamber Music. She died less than five years later, on April 9, 1999.