The transplantation of mesenchymal stem cells (MSCs) proves to be useful to treat pathologies in which tissue damage is linked to oxidative stress (OS). The aim of our work was to evaluate whether primary human MSCs (hMSCs) can manage OS. For this, in vitro we assessed the following parameters: (1) cell viability of hMSCs exposed to increasing concentrations of reactive oxygen species (ROS; source: hydrogen peroxide), reactive nitrogen species (RNS; source: S-nitroso-N-acetylpenicillamine), or both (ROS and RNS; source: 3-morpholinosydnonimine hydrochloride); (2) intracellular level of reactive species in hMSCs exposed to ROS and RNS; (3) basal gene expression and activity of superoxide dismutases, catalase, and glutathione peroxidase of hMSCs; (4) basal level of total glutathione (GSx) of hMSCs; and (5) cell viability of GSx-depleted hMSCs exposed to ROS and/or RNS. Results showed that hMSCs have a high resistance to OS-induced death, which correlates with low levels of intracellular reactive species, constitutive expression of enzymes required to manage OS, and high levels of GSx. When hMSCs were depleted of GSx they lose their capacity to manage OS. Thus, in vitro hMSCs were able to scavenge ROS and RNS and efficiently manage OS. If this potential is maintained in vivo, hMSCs could also contribute to tissue regeneration, limiting OS-induced tissue damage.