Nonlinear all-optical technology is an ultimate route for next-generation ultrafast signal processing of optical communication systems. New nonlinear functionalities need to be implemented in photonics, and complex oxides are considered as promising candidates due to their wide panel of attributes. In this context, yttria-stabilized zirconia (YSZ) stands out, thanks to its ability to be epitaxially grown on silicon, adapting the lattice for the crystalline oxide family of materials. We report, for the first time to the best of our knowledge, a detailed theoretical and experimental study about the third-order nonlinear susceptibility in crystalline YSZ. Via self-phase modulation-induced broadening and considering the in-plane orientation of YSZ, we experimentally obtained an effective Kerr coefficient of ${\widehat{n}}_2^{\mathrm{YSZ}}=4.0\pm 2\times {10}^{?19}{\mathrm{m}}^2·{\mathrm{W}}^{?1}$ in an 8% (mole fraction) YSZ waveguide. In agreement with the theoretically predicted ${\widehat{n}}_2^{\mathrm{YSZ}}=1.3\times {10}^{?19}{\mathrm{m}}^2·{\mathrm{W}}^{?1}$, the third-order nonlinear coefficient of YSZ is comparable with the one of silicon nitride, which is already being used in nonlinear optics. These promising results are a new step toward the implementation of functional oxides for nonlinear optical applications.