Hershko and his family survived the Holocaust. His maternal grandparents disappeared in the Holocaust along with approximately 360,000 Hungarian Jews from Karcag. Hershko emigrated in 1950 from Hungary to Israel. In 1969 he received his doctoral degree at the Hadassah Medical School of the Hebrew University of Jerusalem. He is currently a Professor at the Rappaport Family Institute for Research in Medical Sciences at the Technion (Israel Institute of Technology) in Haifa, Israel.
He was awarded the Israel Prize in 1994, among other things, the Gairdner Foundation International Award in 1999, 2000, Albert Lasker Award for Basic Medical Research and the Alfred P. Sloan, Jr. Prize, the 2001 Massry Prize and the Louisa Gross Horwitz Prize, 2002 EB Wilson Medal and the 2004 Nobel prize in Chemistry for the discovery of ubiquitin-mediated protein degeneration, along with Aaron Ciechanover and Irwin Rose.