The magnetorheological elastomer (MRE) is known to belong to a class of smart materials whose elastic properties can be varied by an externally applied magnetic field. In addition to the property of the field-dependent stiffness change of the MRE, the electrical resistance of the composite is also changed by the induced strain, thereby providing a new self-sensing feature. In the present study, a novel, dynamic vibration absorber is developed using an MRE with a self-sensing function and adaptability. The natural frequency of the absorber is instantaneously tuned to a dominant frequency extracted from the strain signal of MRE. The damping performance test shows that the vibration of a system with one degree-of-freedom that is exposed to a nonstationary disturbance can be adequately reduced by the proposed frequency-tunable dynamic absorber without the use of external sensors.