Shamo was born in Kiev to a family of Jewish origin. He graduated from the Lysenko Music School in Kiev, where his main subjects were composition and piano, in 1941, and was evacuated in that year to Ufa, where he studied medicine for two years. From 1942 to 1946 he was in the Soviet Army as a medical assistant; when he returned to Kiev he recommenced his musical studies, graduating from the Kiev Conservatory in 1951 in the class of Boris Lyatoshinsky. He had joined the Union of Soviet Composers in 1948, and at his graduation played his own Concert-Ballade for piano and orchestra.
His popular song Kyieve Mii (My Kyiv) is regarded as the "unofficial anthem of the Ukrainian capital", and is cited on his memorial on the building where he lived (see picture). His other works include three symphonies, and an opera Yatranskiye Igri, which is unusually scored for a cappella choir and soloists.