Sulfur mustard (SM) and its derivatives are potent genotoxic agents, which have been shown to trigger the activation of poly (ADP-ribose) polymerases (PARPs) and the depletion of their substrate, nicotinamide adenine dinucleotide (NAD+). NAD+ is an essential molecule involved in numerous cellular pathways, including genome integrity and DNA repair, and thus, NAD+ supplementation might be beneficial for mitigating mustard-induced (geno)toxicity. In this study, the role of NAD+ depletion and elevation in the genotoxic stress response to SM derivatives, i.e., the monofunctional agent 2-chloroethyl-ethyl sulfide (CEES) and the crosslinking agent mechlorethamine (HN2), was investigated with the use of NAD+ booster nicotinamide riboside (NR) and NAD+ synthesis inhibitor FK866. The effects were analyzed in immortalized human keratinocytes (HaCaT) or monocyte-like cell line THP-1. In HaCaT cells, NR supplementation, increased NAD+ levels, and elevated PAR response, however, did not affect ATP levels or DNA damage repair, nor did it attenuate long- and short-term cytotoxicities. On the other hand, the depletion of cellular NAD+ via FK866 sensitized HaCaT cells to genotoxic stress, particularly CEES exposure, whereas NR supplementation, by increasing cellular NAD+ levels, rescued the sensitizing FK866 effect. Intriguingly, in THP-1 cells, the NR-induced elevation of cellular NAD+ levels did attenuate toxicity of the mustard compounds, especially upon CEES exposure. Together, our results reveal that NAD+ is an important molecule in the pathomechanism of SM derivatives, exhibiting compound-specificity. Moreover, the cell line-dependent protective effects of NR are indicative of system-specificity of the application of this NAD+ booster.