A gear change device for a motor vehicle has a braking member (L) for stopping the rotation of the primary shaft (10) before engagement of the reverse gear. The braking member comprises a lever (L) pivotally mounted on the gearbox (2) of the gear change device about a separate axis (A3) with respect to the axes (A1, A2) of the primary and secondary shafts (10, 20) of the gear change device. The braking lever (L) is controlled by an electrically-driven actuator (E) by means of a pusher member (P) which is displaceable by said actuator (E) in a direction (t) substantially tangential with respect to the primary shaft (10), towards an operative position in which it interposes with a wedge-like action between the braking lever (L) and a fixed abutment wall (F), so as to press the brake pad (L1) against a cooperating part (M) which is connected in rotation with the primary shaft (10).