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^2/22| = (2.3^+0.6/-0.5) x 10^-3 eV^2 and sin^2(2Ө_23) > 0.93, and maximum mixing is favored.