Born in New York, Feinberg received his undergraduate degree in chemical engineering from The Cooper Union for the Advancement of Science and Art in 1962.
Feinberg was a member of the editorial board of the Archive for Rational Mechanics and Analysis from 1978–1991.
Together with F. J. M. Horn and Roy Jackson, Feinberg created chemical reaction network theory, a field of mathematics that connects the graphical and algebraic structure of chemical reaction networks with their dynamic behavior.
Together with Gheorghe Craciun, he developed the theory of injective reaction networks and explored its implications for biochemistry.
Feinberg is the author of "Foundations of Chemical Reaction Network Theory," published in 2019 by Springer in its Applied Mathematical Sciences series.