We present the first Ge-based constraints on sub-MeV/c^{2} dark matter (DM) particles interacting with electrons using a 33.4 g Ge cryogenic detector with a 0.53 electron-hole pair (rms) resolution, operated underground at the Laboratoire Souterrain de Modane. Competitive constraints are set on the DM-electron scattering cross section, as well as on the kinetic mixing parameter of dark photons down to 1 eV/c^{2}. In particular, the most stringent limits are set for dark photon DM in the 6 to 9 eV/c^{2} range. These results demonstrate the high relevance of Ge cryogenic detectors for the search of DM-induced eV-scale electron signals.