  We show that the new measurement of the effective number of neutrinos Neff by
the Planck satellite can be used to set a robust lower bound on the mass of
cold thermal dark matter of O(MeV). Our limit applies if the dark matter
remains in thermal equilibrium by coupling to electrons and photons or through
interactions with neutrinos, and applies regardless of whether the dark matter
annihilation cross-section is s-wave or p-wave. To illustrate our bounds we
apply them to a model of a supersymmetric neutralino annihilating to neutrinos,
via a light mixed left-right handed sneutrino mediator. While this scenario was
not constrained by previous data, the Planck limits on Neff allow us to set a
lower bound on the neutralino dark matter mass of 3.5 MeV.
