We present results of a dark matter search performed with a 0.6 kg d exposure of the DAMIC experiment at the SNOLAB underground laboratory. We measure the energy spectrum of ionization events in the bulk silicon of charge-coupled devices down to a signal of 60 eV electron equivalent. The data are consistent with radiogenic backgrounds, and constraints on the spin-independent WIMP-nucleon elastic-scattering cross section are accordingly placed. A region of parameter space relevant to the potential signal from the CDMS-II Si experiment is excluded using the same target for the first time. This result obtained with a limited exposure demonstrates the potential to explore the low-mass WIMP region (<10 GeV c-2) with the upcoming DAMIC100, a 100 g detector currently being installed in SNOLAB.