An encapsulated micro-electro-mechanical device, wherein a MEMS chip is encapsulated by a package formed by a first, a second, and a third substrates that are bonded together. The first substrate has a main surface bearing the MEMS chip, the second substrate is bonded to the first substrate and defines a chamber surrounding the MEMS chip, and the third substrate is bonded to the second substrate and upwardly closes the chamber. A grid or mesh structure of electrically conductive material is formed in or on the third substrate and overlies the MEMS chip; the second substrate has a conductive connection structure coating the walls of the chamber, and the first substrate incorporates an electrically conductive region, which forms, together with the conductive layer and the grid or mesh structure, a Faraday cage.