A MEMS sensor, in particular a microphone, of a piezoelectric type, formed in a membrane of semiconductor material accommodating a compliant portion, which extends from a first surface to a second surface of the membrane. The compliant portion has a Young's modulus lower than the rest of the membrane. A sensitive region having piezoelectric material extends on the first surface, over the compliant portion and is fixed at its ends to the membrane on opposite sides of the compliant portion. A third area of the membrane, arranged between the compliant portion and the second surface, forms a hinge element.