In experiments for direct dark matter searches, neutrinos coherently scattering off nuclei can produce similar events as Weakly Interacting Massive Particles (WIMPs). The calculated count rate for solar neutrinos in such experiments is a few events per ton-year. This count rate strongly depends on the nuclear recoil energy threshold achieved in the experiments for the WIMP search. We show that solar neutrinos can be a serious background source for direct dark matter search experiments using Ge, Ar, Xe and CaWO 4 as target materials. To reach sensitivities better than ∼10 −10 pb for the elastic WIMP nucleon spin-independent cross section in the zero-background limit, energy thresholds for nuclear recoils should be ≳2.05 keV for CaWO 4, ≳4.91 keV for Ge, ≳2.89 keV for Xe, and ≳8.62 keV for Ar as target material. Next-generation experiments should not only strive for a reduction of the present energy thresholds but mainly focus on an increase of the target mass. Atmospheric neutrinos limit the achievable sensitivity for the background-free direct dark matter search to ≳10 −12 pb.