A process for manufacturing a MEMS piezoelectric device includes: forming a membrane at a first surface of wafer of semiconductor material further having a second surface (the first and second surfaces being opposite along a vertical axis and extending parallel to a horizontal plane formed by first and second horizontal axes); forming a cavity within the wafer so that the membrane is suspended above the cavity; forming a piezoelectric material layer above a first surface of the membrane; forming an electrode arrangement in contact with the piezoelectric material layer; and forming a proof mass coupled to a second surface of the membrane opposite to the first surface along the vertical axis. The proof mass deforms the membrane in response to environmental mechanical vibrations. Forming the proof mass includes forming a connection element at a central position between the membrane and the proof mass in the direction of the vertical axis.