The IceCube neutrino telescope at the South Pole has measured the atmospheric muon neutrino spectrum as a function of zenith angle and energy in the approximate 320 GeV to 20 TeV range, to search for the oscillation signatures of light sterile neutrinos. No evidence for anomalous νμ or ̅νμ disappearance is observed in either of two independently developed analyses, each using one year of atmospheric neutrino data. New exclusion limits are placed on the parameter space of the 3+1 model, in which muon antineutrinos experience a strong Mikheyev-Smirnov-Wolfenstein-resonant oscillation. The exclusion limits extend to sin²2θ₂₄≤0.02 at Δm²~0.3eV² at the 90% confidence level. The allowed region from global analysis of appearance experiments, including LSND and MiniBooNE, is excluded at approximately the 99% confidence level for the global best-fit value of |Uₑ₄|².