We report results from a reanalysis of data from the Cryogenic Dark Matter Search (CDMS II) experiment at the Soudan Underground Laboratory. Data taken between October 2006 and September 2008 using eight germanium detectors are reanalyzed with a lowered, 2 keV recoil-energy threshold, to give increased sensitivity to interactions from Weakly Interacting Massive Particles (WIMPs) with masses below ~10 GeV/c^2. This analysis provides stronger constraints than previous CDMS II results for WIMP masses below 9 GeV/c^2 and excludes parameter space associated with possible low-mass WIMP signals from the DAMA/LIBRA and CoGeNT experiments.