A MEMS device is provided with: a supporting base, having a bottom surface in contact with an external environment; a sensor die, which is of semiconductor material and integrates a micromechanical detection structure; a sensor frame, which is arranged around the sensor die and is mechanically coupled to a top surface of the supporting base; and a cap, which is arranged above the sensor die and is mechanically coupled to a top surface of the sensor frame, a top surface of the cap being in contact with an external environment. The sensor die is mechanically decoupled from the sensor frame.