A micro-electro-mechanical device, comprising a monolithic body of semiconductor material accommodating a first buried cavity; a sensitive region facing the first buried cavity; a second cavity facing the first buried cavity; a decoupling trench extending from the monolithic body and separating the sensitive region from a peripheral portion of the monolithic body; a cap die, forming an ASIC, bonded to and facing the first face of the monolithic body; and a first gap between the cap die and the monolithic body. The device also comprises at least one spacer element between the monolithic body and the cap die; at least one stopper element between the monolithic body and the cap die; and a second gap between the stopper element and one between the monolithic body and the cap die. The second gap is smaller than the first gap.