The objective this study is to develop the first fully passive nonlinear piezoelectric tuned vibration absorber (NPTVA). The NPTVA is designed to mitigate a specific resonance of a nonlinear host structure. To avoid the use of synthetic inductors which require external power, closed magnetic circuits in ferrite material realize the large inductance values required by vibration mitigation at low frequencies. The saturation of an additional passive inductor is then exploited to build the nonlinearity in the NPTVA. The performance of the proposed device is demonstrated both numerically and experimentally.