  We derive in this Letter the SZ effect induced by the secondary electrons
produced in the annihilation of Weakly Interacting Massive Particles (assumed
here to be neutralinos) in gravitationally bound structures dominated by Cold
Dark Matter (CDM). We show that the DM induced SZ effect has a specific
spectral shape and an amplitude which increases for decreasing neutralino mass
M_{chi}. The available SZ data on the Coma cluster set an upper limit on the
quantity <sigma V> n^2_{chi} which can be combined with the WMAP constraints on
Omega_m h^2 to restrict the available neutralino models in the <\sigma V> -
M_{chi} plane. We delineate various potential applications of this method to
constraint the physical properties of the Dark Matter particles from the study
of galaxy clusters and dwarf spheroidal galaxies in the light of the next
coming high-sensitivity SZ experiments.
