  We show that the high-energy cosmic neutrinos seen by the IceCube Neutrino
Observatory can be used to probe interactions between neutrinos and the dark
sector that cannot be reached by current cosmological methods. The origin of
the observed neutrinos is still unknown, and their arrival directions are
compatible with an isotropic distribution. This observation, together with
dedicated studies of Galactic plane correlations, suggest a predominantly
extragalactic origin. Interactions between this isotropic extragalactic flux
and the dense dark matter (DM) bulge of the Milky Way would thus lead to an
observable imprint on the distribution, which would be seen by IceCube as 1)
slightly suppressed fluxes at energies below a PeV and 2) a deficit of events
in the direction of the Galactic center. We perform an extended unbinned
likelihood analysis using the four-year high-energy starting event dataset to
constrain the strength of DM-neutrino interactions for two model classes. We
find that, in spite of low statistics, IceCube can probe regions of the
parameter space inaccessible to current cosmological methods.
