Michael Anbar was born in the Free City of Danzig on 29 June 1927. He earned his Master's in physical chemistry from Hebrew University in 1950 and in 1953 earned his PhD in physical chemistry from the same institution. That same year, he married his wife Ada on 11 August. Together the had two children, Ran D. and Ariel D. Anbar would later publish papers with both his wife and son.

Anbar held several positions at the Weizmann Institute of Science, starting as a junior research chemist and leaving as associate professor. Anbar has consulted with the Israel Atomic Energy Commission and the Unites Stated Atomic Energy Commission. After serving in a number of positions at the Stanford Research Institute and National Aeronautics and Space Administration Ames Research Center, Anbar joined the University at Buffalo as professor and chairman of the Department of Biophysical Sciences in 1977.

Anbar has also taught in other departments at the University at Buffalo including the Department of Dental Materials and Department of Ophthalmology and the Department of Biophysics at the Roswell Park Memorial Institute. From 1983-1984, Anbar served as Executive Director of the Health-Care Instruments and Device Institute and from 1983-1985 as Associate Dean for Applied Research in the School of Medicine.

Anbar's research interests are in medical instruments, medical education, and the application of computers in medical education.

Michael Anbar retired from the Department of Physiology and Biophysics in 2002 and retains the rank of professor emeritus.