Scheinberg was born in Manhattan and attended DeWitt Clinton High School in the Bronx, New York City; he won a place at Harvard University, graduating with a bachelor's degree in chemistry in 1940.
Scheinberg then began his academic career back at Harvard and joined the Albert Einstein College of Medicine upon its foundation in 1955.
While Scheinberg was a faculty member at Albert Einstein College of Medicine, he, Irmin Sternlieb and John Walshe of Cambridge University researched the use of penicillamine as a treatment for Wilson's Disease.
Scheinberg's first wife, Tess Levine, died of a brain tumor shortly after giving birth to their daughter Anne.
Scheinberg enjoyed astronomy and traveled great distances to witness all major eclipses of the sun.