We report a first search for weakly interacting massive particles (WIMPs) using the background rejection capabilities of SuperCDMS. An exposure of 577 kg days was analyzed for WIMPs with mass <30GeV/c2, with the signal region blinded. Eleven events were observed after unblinding. We set an upper limit on the spin-independent WIMP-nucleon cross section of 1.2×10-42cm2 at 8GeV/c2. This result is in tension with WIMP interpretations of recent experiments and probes new parameter space for WIMP-nucleon scattering for WIMP masses <6GeV/c2.