We employ data from the recently observed high-energy neutrino events at the IceCube Neutrino Observatory to constrain interactions between the dark matter (DM) in the Milky Way and the neutrino sector. We construct an extended un-binned likelihood in order to explore the parameter space of allowed interactions. We present results in the specific case of a scalar DM candidate interacting via a scalar mediator, and show that due to the energy dependence of the interaction cross section, this approach can constrain the coupling more strongly than traditional cosmological probes for some regions of the parameter space.