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 \times 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 } .