A MEMS actuator device of a piezoelectric type formed on a substrate, with a base unit including a base beam element having a main extension in a extension plane and a thickness in a thickness direction perpendicular to the extension plane, smaller than the main extension. A piezoelectric region extends over the beam element. An anchor region is rigid to the base beam element and to the substrate. A base constraint structure is connected to one end of the base beam element and is configured to allow a deformation of the base beam element in the extension plane and substantially reduce a deformation of the base beam element in the thickness direction.