  The 2-years MESE IceCube events show a slightly excess in the energy range
10-100 TeV with a maximum local statistical significance of 2.3$\sigma$, once a
hard astrophysical power-law is assumed. A spectral index smaller than 2.2 is
indeed suggested by multi-messenger studies related to $p$-$p$ sources and by
the recent IceCube analysis regarding 6-years up-going muon neutrinos. In the
present paper, we propose a two-components scenario where the extraterrestrial
neutrinos are explained in terms of an astrophysical power-law and a Dark
Matter signal. We consider both decaying and annihilating Dark Matter
candidates with different final states (quarks and leptons) and different halo
density profiles. We perform a likelihood-ratio analysis that provides a
statistical significance up to 3.9$\sigma$ for a Dark Matter interpretation of
the IceCube low energy excess.
