  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$\times$10$^{-22}$ A cm$^{-2}$. We evaluate the charge distribution of
pixels that collect $<10~\rm{e^-}$ 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$c^{-2}$.
