The covering element has a visible face and an invisible face opposite the visible face. It includes a weakening line which is formed on the invisible face and defines a gate zone which is to open under the pressure of the deployment of the airbag when the motor vehicle is subjected to an impact. The weakening line includes a groove which has a given total length and is delimited by a bottom and at least one transverse rib which projects relative to the bottom and closes the groove at least partially. The covering element has a thickness of material between the visible face and the bottom which is between predetermined minimum and maximum limits over most of the total length of the groove. The groove includes at least one zone of lesser strength in which the thickness of material between the visible face and the bottom is less than the minimum limit.