A microelectromechanical device includes a substrate, a first structural layer, and a second structural layer of semiconductor material. A sensing mass extends in the first structural layer and is coupled to the substrate by first elastic connections to enable oscillation of the sensing mass in a sensing direction perpendicular to the substrate by a maximum amount relative to a resting position of the sensing mass. An out-of-plane stopper structure includes an anchorage fixed to the substrate and a mechanical end-of-travel structure, which extends in the second structural layer, faces the sensing mass, and is separated therefrom by a gap having a width smaller than the maximum displacement distance of the sensing mass. The mechanical end-of-travel structure is coupled to the anchorage by second elastic connections that enable movement of the mechanical end-of-travel structure in the sensing direction in response to an impact of the sensing mass.