We present the first statistically significant detection of neutrino oscillations in the high-energy regime (> 20 GeV) from an analysis of IceCube Neutrino Observatory data collected in 2010 and 2011. This measurement is made possible by the low-energy threshold of the DeepCore detector (similar to 20 GeV) and benefits from the use of the IceCube detector as a veto against cosmic-ray-induced muon background. The oscillation signal was detected within a low-energy muon neutrino sample (20-100 GeV) extracted from data collected by DeepCore. A high-energy muon neutrino sample (100 GeV-10 TeV) was extracted from IceCube data to constrain systematic uncertainties. The disappearance of low-energy upward-going muon neutrinos was observed, and the nonoscillation hypothesis is rejected with more than 5 sigma significance. In a two-neutrino flavor formalism, our data are best described by the atmospheric neutrino oscillation parameters vertical bar Delta m(32)(2)vertical bar = (2.3(-0.5)(+0.6)) x 10(-3) eV(2) and sin(2) (2 theta(23)) > 0.93, and maximum mixing is favored.