Hershko was born Herskó Ferenc in Karcag, Hungary, the son of Shoshana Margit and Moshe Hershko, both teachers. Hershko emigrated to Israel in 1950. He received his M.D. in 1965 and his Ph.D in 1969 from the Hebrew University-Hadassah Medical School, Jerusalem, Israel. He is currently a Distinguished Professor at the Rappaport Faculty of Medicine at the Technion in Haifa.
Along with Aaron Ciechanover and Irwin Rose, he was awarded the 2004 Nobel Prize in Chemistry for the discovery of ubiquitin-mediated protein degradation. The ubiquitin-proteasome pathway has a critical role in maintaining the homeostasis of cells and is believed to be involved in the development and progression of diseases such as cancer, muscular and neurological diseases, and immune and inflammatory responses.
His contributions to science directly helped cure one of his long-time friends of cancer. 
Hershko, A., Ciechanover, A., Heller, H., Haas, A.L., and Rose I.A. (1980) "Proposed role of ATP in protein breakdown: Conjugation of proteins with multiple chains of the polypeptide of ATP-dependent proteolysis". Proc. Natl. Acad. Sci. USA 77, 1783–1786.
Hershko, A., Heller, H., Elias, S. and Ciechanover, A. (1983) Components of ubiquitin-protein ligase system: resolution, affinity purification and role in protein breakdown. J. Biol. Chem. 258, 8206–8214.
Hershko, A., Leshinsky, E., Ganoth, D. and Heller, H. (1984) ATP-dependent degradation of ubiquitin-protein conjugates. Proc. Natl. Acad. Sci. USA 81, 1619–1623.
Hershko, A., Heller, H., Eytan, E. and Reiss, Y. (1986) The protein substrate binding site of the ubiquitin-protein ligase system. J. Biol. Chem. 261, 11992-11999.
Ganoth, D., Leshinsky, E., Eytan, E., and Hershko, A. (1988) A multicomponent system that degrades proteins conjugated to ubiquitin. Resolution of components and evidence for ATP-dependent complex formation. J. Biol. Chem. 263, 12412-1241.
Sudakin, V., Ganoth, D., Dahan, A., Heller, H., Hershko, J., Luca, F.C., Ruderman, J.V. and Hershko, A. (1995). The cyclosome, a large complex containing cyclin-selective ubiquitin ligase activity, targets cyclins for destruction at the end of mitosis. Mol. Biol. Cell 6, 185–198.