The ultra-light dark matter is a new class of dark matter candidates. Unlike traditional dark matter particle candidates, the ultra-light dark matter behaves like a classical field, and it saturates the entire Milky Way galaxy with a coherent oscillation. If such dark matter exists and couples with neutrinos, properties of astrophysical neutrinos propagating in the Milky Way would be modified and detectable by neutrino telescopes such as IceCube. Meantime, IceCube looked for quantum-gravity-motivated effects from the astrophysical neutrino flavour information. IceCube did not find evidence of new physics, and they set limits on neutrino - Lorentz violating field couplings. Here, we investigate if these results can be applied to limit the ultra-light dark matter couplings with neutrinos. It is found that the strong limits of neutrino-dark matter couplings in low dark matter mass regions can be obtained in this approach.