In this study, ultrafast third-order optical nonlinearity of ZnO crystals with different crystal planes and doping under femtosecond linearly/radially polarized light (330 fs, 532 nm) excitation is investigated. First, the band gap of ZnO crystals is analyzed using an ultraviolet-visible spectroscopy absorption spectrum. Next, the third-order optical nonlinearity of the ZnO crystals under femtosecond linearly/radially polarized light is measured using the Z-scan technique. The results show that the nonlinear saturation absorption effect and self-focusing effect are observed in ZnO crystals with different crystal planes and doping under the excitation of linearly and radially polarized lights owing to the electron transition in the defect state of the ZnO crystals. The third-order optical nonlinearity of ZnO[101] is the strongest for femtosecond linearly polarized light excitation, owing to the third-order optical nonlinearity of near-resonance enhancement caused by the narrowed energy bandgap in ZnO crystals. However, under the excitation of radially polarized light, ZnO[110] has the strongest third-order optical nonlinearity, probably owing to the combination of the narrow energy bandgap and the anisotropic nonlinearity caused by the axisymmetric polarization of the femtosecond vector laser. This study has potential application value in saturable absorbers, ultrafast light field regulation, and super-resolution imaging.