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 <30 GeV/c(2), 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(-42) cm(2) at 8 GeV/c(2). This result is in tension with WIMP interpretations of recent experiments and probes new parameter space for WIMP-nucleon scattering for WIMP masses <6 GeV/c(2).