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 |Δm232|=(2.3+0.6−0.5)×10−3  eV2 and sin2(2θ23)>0.93, and maximum mixing is favored.