A MEMS transducer has a micromechanical sensing structure and a package. The package is provided with a substrate, carrying first electrical-connection elements, and with a lid, coupled to the substrate to define an internal cavity, in which the micromechanical sensing structure is housed. The lid is formed by: a cap layer having a first surface and a second surface, set opposite to one another, the first surface defining an external face of the package and the second surface facing the substrate inside the package; and a wall structure, set between the cap layer and the substrate, and having a coupling face coupled to the substrate. At least a first electrical component is coupled to the second surface of the cap layer, inside the package, and the coupling face of the wall structure carries second electrical-connection elements, electrically connected to the first electrical component and to the first electrical-connection elements.