The MEMS device (20) is formed by a substrate (21) and a movable structure (22) suspended on the substrate. The movable structure has a first mass (28), a second mass (29A) and a first elastic group (30A) mechanically coupled between the first and the second masses. The first elastic group is compliant along a first direction (Y). The first mass is configured to move with respect to the substrate along the first direction. The MEMS device also has a second elastic group (23) mechanically coupled between the substrate and the movable structure and compliant along the first direction; and an anchoring control structure (33A, 40A) fixed to the substrate, capacitively coupled to the second mass and configured to exert an electrostatic force on the second mass along the first direction. The anchoring control structure controls the MEMS device in a first operating state, wherein the second mass is free to move with respect to the substrate along the first direction, and in a second operating state, wherein the anchoring control structure applies a pull-in force on the second mass which anchors the second mass to the anchoring control structure.