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 (~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 5σ significance. In a two-neutrino flavor formalism, our data are best described by the atmospheric neutrino oscillation parameters |Δm(32)(2)|=(2.3(-0.5)(+0.6))×10(-3) eV(2) and sin(2)(2θ(23))>0.93, and maximum mixing is favored.