The next generation of solar neutrino detectors will provide a precision measure of the 8 B electron-neutrino spectrum in the energy range from 1-15 MeV. Although the neutrino spectrum emitted by 8 B β-decay reactions in the Sun's core is identical to the neutrino spectrum measured in the laboratory, due to vacuum and matter flavor oscillations, this spectrum will be very different from that measured on Earth by the different solar neutrino experiments. We study how the presence of dark matter (DM) in the Sun's core changes the shape of the 8 B electron-neutrino spectrum. These modifications are caused by local variations of the electronic density and the 8 B neutrino source, induced by local changes of the temperature, density and chemical composition. Particularly relevant are the shape changes at low and medium energy range (E ν ≤ 10 MeV), for which the experimental noise level is expected to be quite small. If such a distortion in the 8 Bν e spectrum were to be observed, this would strongly hint in favor of the existence of DM in the Sun's core. The 8 B electron-neutrino spectrum provides a complementary method to helioseismology and total neutrino fluxes for constraining the DM properties. In particular, we study the impact of light asymmetric DM on solar neutrino spectra. Accurate neutrino spectra measurements could help to determine whether light asymmetric DM exists in the Sun's core, since it has been recently advocated that this type of DM might resolve the solar abundance problem.