A metering servovalve for a fuel injector of an internal combustion engine has an electro-actuator and a fixed valve body, which defines a control chamber communicating with an inlet and with an outlet channel. The outlet channel has at least one calibrated restriction and exits through the lateral surface of an axial stem, on which a sleeve slides, in a substantially fluid-tight manner, to open/close the outlet channel and so vary the pressure in the control chamber. The outlet channel is closed by an end portion of the sleeve that is elastically deformable in a radially outward direction, under the thrust of the fuel pressure, to increase the diameter at which the seal against the valve body is formed, with respect to a non-deformed state, and to generate an axial unbalancing force on the sleeve upon opening when the outlet channel is closed.