A fuel injector has an injector body and a control rod, which is movable in the injector body along an axis to control the opening/closing of a nozzle that injects fuel into a cylinder of the engine; the injector body houses a metering servovalve having a control chamber, which is axially delimited by the control rod and communicates with an inlet and with a discharge channel; the metering servovalve is provided with a shutter, which slides axially on an axial guide, from which the discharge channel exits, to open and close the discharge channel and, in consequence, vary the pressure in the control chamber; the discharge channel has three restrictions having calibrated passage sections and arranged in series with each other to divide the pressure drop along the discharge channel.