We report direct-detection constraints on light dark matter particles interacting with electrons. The results are based on a method that exploits the extremely low levels of leakage current of the DAMIC detector at SNOLAB of 2-6×10 −22 A cm −2 . We evaluate the charge distribution of pixels that collect < 10 e − for contributions beyond the leakage current that may be attributed to dark matter interactions. Constraints are placed on so-far unexplored parameter space for dark matter masses between 0.6 and 100 MeV c −2 . We also present new constraints on hidden-photon dark matter with masses in the range 1.2-30 eV c −2 .There is overwhelming astrophysical and cosmological evidence for Dark Matter (DM) as a major constituent of the universe. Still, its nature remains elusive. The compelling Weakly Interacting Massive Particle (WIMP) dark matter paradigm [1] -implying DM is made of hitherto unknown particles with mass in the GeV-TeV scale -has been intensely scrutinized during the last two decades by detectors up to the tonne-scale looking for nuclear recoils induced by coherent scattering of WIMPs. Despite the impressive improvements in sensitivity, notably by noble liquid experiments [2], WIMPs have so far escaped detection. Other viable candidates include DM particles from a hidden-sector [3], which couple weakly with ordinary matter through, for example, mixing of a hidden-photon with an ordinary photon [4]. A phenomenological consequence is that hiddensector DM particles also interact with electrons, with sufficiently large energy transfers to be detectable down to DM masses of ≈ MeV [5]. Also, eV-mass hidden-photon DM particles can be probed through absorption by electrons in detection targets [The DAMIC (Dark Matter in CCDs) experiment [7] is well-suited for a sensitive search of this class of DM candidates. DAMIC detects ionization events induced in the bulk silicon of thick, fully depleted Charge Coupled Devices (CCDs). By exploiting the charge resolution of the CCDs (≈ 2 e − ) and their extremely low leakage current (≈ 4 e − mm −2 d −1 ), DAMIC has already placed constraints on hidden-photon DM with masses in the range 1.2-30 eV c −2 [8] with data collected during the experiment's commissioning phase. In this Letter we apply a similar approach to explore DM-e − interactions with high-quality data from the DAMIC science run at the SNOLAB underground laboratory. We also present improved limits on hidden-photon DM particles.To model DM-e − interactions we follow Ref.[9] where the bound nature of the electrons and crystalline band structure of the target are properly taken into account. The differential event rate in the detector for a DM mass m χ , with transferred energy E e , and momentum q is parametrized as dR dE e ∝σ e dq q 2 η(m χ , q, E e )|F DM (q)| 2 |f c (q, E e )| 2 , (1) whereσ e is a reference cross section for free electron arXiv:1907.12628v1 [astro-ph.CO]