Climate change is expected to increase temperatures and decrease precipitation in the Mediterranean Sea (MS) basin, causing substantial changes in the thermohaline circulation (THC) of both the Western Mediterranean Sea (WMS) and Eastern Mediterranean Sea (EMS). The exact nature of future circulation changes remains highly uncertain, however, with forecasts varying from a weakening to a strengthening of the THC. Here we assess the sensitivity of dissolved oxygen (O2) distributions in the WMS and EMS to THC changes using a mass balance model, which represents the exchanges of O2 between surface, intermediate, and deep water reservoirs, and through the Straits of Sicily and Gibraltar. Perturbations spanning the ranges in O2 solubility, aerobic respiration kinetics, and THC changes projected for the year 2100 are imposed to the O2 model. In all scenarios tested, the entire MS remains fully oxygenated after 100 years; depending on the THC regime, average deep water O2 concentrations fall in the ranges 151–205 and 160–219 µM in the WMS and EMS, respectively. On longer timescales (>1000 years), the scenario with the largest (>74%) decline in deep water formation rate leads to deep water hypoxia in the EMS but, even then, the WMS deep water remains oxygenated. In addition, a weakening of THC may result in a negative feedback on O2 consumption as supply of labile dissolved organic carbon to deep water decreases. Thus, it appears unlikely that climate‐driven changes in THC will cause severe O2 depletion of the deep water masses of the MS in the foreseeable future.