This letter focuses on the problem of handling impacts by means of an aerial manipulator and proposes a solution that combines the control of the aerial manipulator's end-effector position with an innovative design approach of aerial manipulation systems, consisting of both active and passive joints. The approach aims at limiting the influence of impacts on the controlled attitude dynamics in order to allow the aerial manipulator to remain stable during and after impact. The developed concept is intended to convert kinetic energy into potential energy, which is permanently stored into elastic elements by means of directional locking mechanisms. The proposed approach has been tested on a 2 d.o.f. manipulator mounted on a quadrotor UAV. The manipulation system has one active rotational d.o.f. compensating for pitch movements of the UAV and one passive linear joint which is in charge of absorbing the impact energy. The device has been used to validate the method through experiments, in comparison with a rigid manipulator. The results show that the proposed approach and the developed mechanical system achieve stable impact absorption without bouncing away from the interacting environment. Our work has the ambition to propose a new direction towards aerial manipulators that are capable of performing highly dynamic physical interaction tasks.