He was educated at Wagner’s and at Eton College. His undergraduate studies were delayed for four years by World War II. He came up to King's College in 1945, studying History before changing to English. After Cambridge, he studied art history at the Courtauld Institute. This was followed by research at Harvard on Rubens and his contemporaries.
Michael began a fellowship at King’s College in 1952, then he worked as a professor of Renaissance art at Washington University in St. Louis in 1960. In 1961 he returned to England’s Cambridge University, first as a lecturer until 1968, then as a reader, followed by stints as professor in the history of Western art and head of the department.
In 1973 he was named director of Fitzwilliam Museum, where he worked until his retirement in 1990. During his career, Jaffe was famous for acquiring precious works of art for various museums. Among his acquisitions were Van Dyck’s “Madonna and Child” and Renoir’s “Place Clichy.” Among his other books are "Rubens and Italy" and "Jordaens." Jaffe also edited "The Devonshire Collection of Italian Orawings."
Jaffé married Patricia Milne-Henderson in 1964, and they had two sons and two daughters.