  We study oscillations of the high energy atmospheric neutrinos in the Earth
into sterile neutrinos with the eV-scale mass. The MSW resonance and parametric
enhancement of the $\bar{\nu}_\mu\to\bar{\nu}_s$ oscillations lead to
distortion of the zenith angle distribution of the muon-track events which can
be observed by IceCube. Due to matter effect, the IceCube signal depends not
only on the mixing element $U_{\mu 4}$ relevant for LSND and MiniBooNE but also
on $U_{\tau 4}$ and the CP-violating phase $\delta_{24}$. We show that the case
with $U_{\tau 4} = \delta_{24} = 0$ leads to the weakest IceCube signal and
therefore should be used to bound $U_{\mu 4}$. We compute the zenith angle
distributions of the $\nu_\mu-$events for different energy intervals in the
range (0.1 - 10) TeV and find that inclusion of the energy information (binning
in energy) improves the sensitivity to $\nu_s$ drastically. We estimate that
with already collected (during 3 - 4 years) IceCube statistics the bound
$|U_{\mu 4}|^2 < 0.01$ ($99\%$ C.L.) can be established and the mixing required
by LSND and MiniBooNE can be excluded at $(4 - 6) \sigma$ confidence level.
