Eigen received his Ph.D. at the University of Göttingen in 1951 under supervision of Arnold Eucken. From 1953 on he worked at the Max Planck Institute for Physical Chemistry in Göttingen, becoming its Director in 1964 and joining it with the Max Planck Institut for Spectroscopy to become the Max Planck Institute for Biophysical Chemistry. He is an honorary professor of the Braunschweig University of Technology. From 1982 to 1993, Eigen was President of the German National Merit Foundation. Eigen is currently a member of the Board of Sponsors of The Bulletin of the Atomic Scientists.
In 1967, Eigen was awarded, along with Ronald George Wreyford Norrish and George Porter, the Nobel Prize in Chemistry. They were distinguished for their studies of extremely fast chemical reactions induced in response to very short pulses of Energy.
In addition, Eigen's name is linked with the theory of quasispecies, the error threshold, error catastrophe, Eigen's paradox, and the chemical hypercycle, the cyclic linkage of reaction cycles as an explanation for the self-organization of prebiotic systems, which he described with Peter Schuster in 1977. He founded two biotechnology companies, Evotec and Direvo.
In 1981, Eigen became a founding member of the World Cultural Council.