Murad was born in Whiting, Indiana, and graduated as an MD from the Western Reserve University School of Medicine, Cleveland, Ohio, in 1965. Three years later he gained his PhD from the department of pharmacology at the same university. He has held many important appointments; since 1988 he has worked at the Northwestern University Medical School, Chicago, Illinois. In 1998 he shared the Nobel Prize for physiology or medicine with Robert Furchgott and Louis Ignarro for their discovery that molecules of the gas nitrogen monoxide (nitric oxide, NO) can transmit signals in the cardiovascular system.

The hitherto unknown substance endothelium-derived relaxing factor (EDRF) had been discovered by Furchgott in 1980. Murad researched the action of glyceryl trinitrate (nitroglycerin) and related vasodilators, and in 1977 discovered that they release nitrogen monoxide, which relaxes the walls of smooth muscle cells. It thus has the effect of controlling the blood pressure and this is why glyceryl trinitrate is prescribed as a drug to treat the heart condition atherosclerosis (as ironically it once was for Alfred Nobel, who invented the nitroglycerin-containing dynamite). Murad also speculated that hormones and other endogenous factors might act in a similar way, although no evidence of this was forthcoming.