A MEMS device wherein a die of semiconductor material has a first face and a second face. A diaphragm is formed in or on the die and faces the first surface. A cap is fixed to the first face of the die and has a hole forming a fluidic path connecting the diaphragm with the outside world. A closing region, for example a support, a second cap, or another die, is fixed to the second face of the die. The closing region forms, together with the die and the cap, a stop structure configured to limit movements of the suspended region in a direction perpendicular to the first face.