A search for sidereal modulation in the flux of atmospheric muon neutrinos in IceCube was performed. Such a signal could be an indication of Lorentz-violating physics. Neutrino oscillation models, derivable from extensions to the standard model, allow for neutrino oscillations that depend on the neutrino's direction of propagation. No such direction-dependent variation was found. A discrete Fourier transform method was used to constrain the Lorentz and CPT-violating coefficients in one of these models. Because of the unique high energy reach of IceCube, it was possible to improve constraints on certain Lorentz-violating oscillations by 3 orders of magnitude with respect to limits set by other experiments.