Impact may excite intense vibration responses of the flexible robotic arm and thus deteriorate its working performance. A vibration absorption method is put forward to alleviate impact influence of the flexible robotic arm. To dissipate the impact vibration energy, a slider mass–spring–dashpot mechanism is used as a vibration absorber and attached to the flexible robotic arm. Internal resonance is sufficiently utilized to provide a bridge for the transfer of impact vibration energy between the flexible link and the absorber via nonlinear coupling. In the presence of damping of the absorber, the impact vibration energy of the flexible link can be effectively migrated to and dissipated by the absorber. Numerical simulations and virtual prototype simulations verify its effectiveness and feasibility in alleviating impact vibration of the flexible robotic arm undergoing a collision.