A microelectromechanical membrane transducer includes: a supporting structure; a cavity formed in the supporting structure; a membrane coupled to the supporting structure so as to cover the cavity on one side; a cantilever damper, which is fixed to the supporting structure around the perimeter of the membrane and extends towards the inside of the membrane at a distance from the membrane; and a damper piezoelectric actuator set on the cantilever damper and configured so as to bend the cantilever damper towards the membrane in response to an electrical actuation signal.