An object self-protection apparatus (12) having a monitoring device (14) which is fixed with respect to the object and a launch container (18), in particular for fragmentation projectiles, which has a target-tracking radar device (20) for the approach movement of a missile (22) which is to be defended against. The monitoring device (14) which is fixed with respect to the object and the target-tracking radar device (20) are connected together with an aiming drive for the launch container (18). Hereby, an expensive search radar is replaced by a passive sensor device (16) forming the monitoring device (14) which is fixed with respect to the object. The passive sensor device (16) generates accurately measured angular information in respect of the approaching missile (22). The distance and the speed of the missile (22) are then determined by the target-tracking radar device (20).