A solenoid valve for controlling a fuel injector of an internal combustion engine, including an electromagnet, a movable armature featuring an armature plate and an armature pin, as well as a control valve member, which is moved with the armature and cooperates with a valve seat, for opening and closing a fuel discharge passage of a control pressure chamber of the fuel injector, the armature plate being supported on the armature pin, so that it is slidably movable in the closing direction of the control valve member under the action of its inertial mass, against the elastic force of a return spring that acts upon the armature plate; and including a hydraulic damping device which permits damping of a post-oscillation of the armature plate during its dynamic sliding on the armature pin. To facilitate the assembly and reduce a disadvantageous post-oscillation process of the armature plate, it is proposed for the return spring to be braced, with its end facing away from the armature plate, against a supporting piece, which is mounted on and moved with the armature pin and which, at the same time, constitutes a part of the damping device.