The ultrafast changes of material properties induced by short laser pulses can lead to a frequency shift of reflected and transmitted radiation. Recent reports highlight how such a frequency shift is enhanced in spectral regions where the material features a near-zero real part of the permittivity. Here, we investigate the frequency shift for fields generated by four-wave mixing. In our experiment, we observed a frequency shift of more than 60 nm (compared to the pulse width of ∼40 nm) in the phase conjugated radiation generated by a 500 nm aluminium-doped zinc oxide (AZO) film pumped close to the epsilon-near-zero wavelength. Our results indicate applications of time-varying media for nonlinear optics and frequency conversion.