A method for making an integrated micro-electromechanical device includes forming a first body of semiconductor material having a first face and a second face opposite the first face. The first body includes a buried cavity forming a diaphragm delimited between the buried cavity and the first face. The diaphragm is monolithic with the first body. The method further includes forming at least one first magnetic via extending between the second face and the buried cavity of the first body, forming a first magnetic region extending over the first face of the first body, and forming a first coil extending over the second face of the first body and being magnetically coupled to the first magnetic via.