  We compute the one-loop effects on the neutrino propagation through matter
induced by virtual supersymmetric particles. We show that, in the minimal
version of the supersymmetric standard model, a non-degeneracy between sleptons
of the second and third generations can have sizeable effects on the
$\nu_\mu$--$\nu_\tau$ oscillations in matter. In particular, we discuss how
this could affect the detection of the energetic neutrino fluxes arising from
annihilation of supersymmetric dark matter in the center of the sun.
