Continental margin sediments contain large reservoirs of methane stored as gas hydrate. Ocean warming will partly destabilize these reservoirs which may lead to the release of substantial, yet unconstrained, amounts of methane. Anaerobic oxidation of methane is the dominant biogeochemical process to reduce methane flux, estimated to consume 90% of the methane produced in marine sediments today. This process is however neglected in the current projections of seafloor methane release from gas hydrate dissociation. Here, we introduce a fully coupled oxidation module to a hydraulic-thermodynamic-geomechanical hydrate model. Our results show that for seafloor warming rates > 1 degrees C century(-1), the efficiency of anaerobic oxidation of methane in low permeability sediments is poor, reducing the seafloor methane emissions by <5%. The results imply an extremely low mitigating effect of anaerobic oxidation of methane on climate warming-induced seafloor methane emissions. Microbial anaerobic oxidation of methane may not substantially mitigate projected warming-induced emissions of methane from marine hydrate-bearing sediments, according to a coupled hydraulic-thermodynamic-geomechanical hydrate model.