The objective of this study is to develop a fully passive nonlinear piezoelectric vibration absorber that mitigates a specific resonance of a nonlinear system. To this end, the saturation of a passive inductor based on a magnetic circuit in ferrite material is exploited to realize the nonlinearity in the absorber. The resulting variable inductance generates an autonomous adjustment of the shunt resonance frequency. The performance of the proposed device is demonstrated numerically and experimentally.