Reizen was born into a Jewish family of mine workers in 1895 at Zaitsevo village in Yekaterinoslav Governorate. He had four brothers and a sister, and all were trained in music, playing mandolin, guitar, balalaika and accordion. He served as a soldier in the First World War. He studied engineering at the Kharkiv Politechnic, and also voice at the Kharkiv Conservatory with the Italian professor Federico Bugamelli in 1919–1920. He debuted at the Kharkiv Opera in 1921 as Pimen in Mussorgsky's Boris Godunov, and in 1925 moved to the Mariinsky Theatre in Leningrad. Reizen toured Europe performing in Paris, Berlin, Monte Carlo and London in 1929–1930.
In 1967 he began teaching, and became a professor at Moscow's Gnessin Institute. He gave an important recital for his 80th birthday, and for his 90th sang Prince Gremin (in Eugene Onegin) at the Bolshoi in Moscow in July 1985. On both occasions, his voice sounded remarkably preserved.
Reizen died of a stroke in 1992 in Moscow at the age of 97. A number of his recordings are still available on CD, and film clips of his performances also exist.