Milstein was born at Bahia Blanca in Argentina and attended the University of Buenos Aires, receiving his degree in 1952 and his doctorate in 1957. Three years later he was granted a PhD by Cambridge University. Milstein returned to his native Argentina in 1961 to head the Molecular Biology Division of the Instituto Nacional de Microbiologiá in Buenos Aires. In 1963 he joined the staff of the Medical Research Council's Laboratory of Molecular Biology in Cambridge and in 1983 he was appointed head of the Division of Protein and Nucleic Acid Chemistry, a post in which he remained until his retirement in 1994.

Milstein is best known for producing the first monoclonal antibodies, using a technique developed at the MRC's Laboratory in collaboration with the German immunologist, George Köhler, and first reported by them in 1975. The pair went on to show how it was possible to manufacture quantities of antibody of any desired specificity employing cultures of so-called ‘hybridoma’ cells. Monoclonal antibodies have found wide-ranging application in biology, medicine, and industry, especially for diagnostic tests and assays. For his part in developing this revolutionary technology, Milstein was awarded the 1984 Nobel Prize for physiology or medicine, which he shared with Köhler and Niels Jerne.