β-Nicotinamide adenine dinucleotide (NAD+) and its reduced form (NADH) play major roles in the development of electrochemical enzyme biosensors and biofuel cells. Unfortunately, the oxidation of NADH at carbon electrodes suffers from passivation of the electrodes and a decrease in passing currents. Here, we investigate experimentally and theoretically the reasons for such passivation. High-resolution X-ray photoelectron spectroscopy (HR-XPS), voltammetry, and amperometry show that adsorption occurs on the edges and “edge-like” defects of graphene sheets. HR-XPS and ab initio molecular dynamics show that the adsorption of NAD+ molecules on the edges of graphene happens due to interaction with oxygen-containing groups such as carboxylic groups, while graphene edges substituted only with hydrogen are prone to passivation.