The increase of temperature of a low‐permeability, fluid‐saturated media may trigger significant thermal pressurization, where the expansion of pore fluid cannot be accommodated by the thermal expansion of the pore space. With the aid of a coupled thermohydromechanical numerical simulator, we investigate the possible impact of thermal pressurization during the life of a deep geological repository (DGR) for high‐level radioactive waste, characterized by the emplacement of radioactive material‐filled canisters in a series of parallel tunnels, excavated in a low‐permeability clay formation. We represent the fault as a planar structure embedded in a thermoporoelastic material and shear activation evaluated by a strain‐softening Mohr‐Coulomb failure criterion. The results show that stress changes caused by temperature and thermal pressurization of a rock mass around the emplacement tunnels may trigger a slip event on a fault plane in proximity of the geological disposal site: Rupture nucleates at depth, hundreds of meters below the DGR. Stress transfer plays a key role, while a direct hydraulic connection between the repository and the nucleation zone is not necessary in order to trigger rupture. A low stress ratio may favor the occurrence of slip up to a distance of 600 m of the fault from the outermost tunnel. These results highlight the need of investigating hydromechanical properties and local stress conditions at depth to characterize the geomechanical response of weak planes located in the surroundings of a high‐level radioactive waste repository and to provide sufficient knowledge for the safe development of the DGR site.