We compute the non-thermal emissions produced by relativistic particles accelerated by the shocks driven by the active galactic nucleus (AGN) in NGC 1068, and we compare the model predictions with the observed γ-ray and radio spectra. The former is produced by pion decay, inverse Compton scattering, and bremsstrahlung, while the latter is produced by synchrotron radiation. We derive the γ-ray and radio emissions by assuming the standard acceleration theory, and we discuss how our results compare with those corresponding to other commonly assumed sources of γ-ray and radio emissions, like supernova remnants (SNR) or AGN jets. We find that the AGN-driven shocks observed in the circumnuclear molecular disk of NGC 1068 provide a contribution to the γ-ray emission comparable to that provided by the starburst activity when standard particle acceleration efficiencies are assumed, while the shocks can yield the whole γ-ray emission only when the parameters describing the acceleration efficiency and the proton coupling with the molecular gas are tuned to values larger than those assumed in standard, SNR-driven shocks. We discuss the range of acceleration efficiencies (for protons and electrons) and of proton calorimetric fractions required to account for the observed γ-ray emission in the AGN outflow model. We further compare the neutrino flux expected in our model with constraints from current experiments, and we provide predictions for the detections by the upcoming KM3NeT neutrino telescope. This analysis strongly motivates observations of NGC 1068 at ≳TeV energies with current and future Cherenkov telescopes in order to gain insight into the nature of the γ-rays source.