Gauging the muon lepton flavor minus the tau lepton flavor number, which is a global symmetry of the SM, introduces a new gauge boson Z' upon symmetry breaking. Interestingly, it offers an economical solution to the long-standing g_µ-2 anomaly, confirmed and strengthened by recent measurements at Fermilab. Here, we revisit the impact of such a Z' on the spectrum of high-energy astrophysical neutrinos, as measured by the IceCube experiment. This spectrum has been observed to exhibit a dip-like feature at sub-PeV energies, which could plausibly arise from the physics of the sources themselves, but could also be the consequence of high-energy neutrinos resonantly scattering with the cosmic neutrino background, mediated by a Z' with a mass on the order of m_Z’ ~ 10 MeV. In this study, we calculate the impact of such a Z' on the high-energy neutrino spectrum for a variety of model parameters and source distributions. For couplings that can resolve the g-2 anomaly, we find that this model could self-consistently produce a spectral feature that is consistent with IceCube's measurement, in particular if the neutrinos observed by IceCube predominantly originate from high-redshift sources. We also briefly discuss a possible scenario where Z' could act as a portal to a dark sector.