Non-standard neutrino interactions affect the propagation of atmospheric neutrinos through the Earth. While most previous analyses have focused on relatively low-energy, $\cal{O}$(10 GeV), atmospheric neutrino data, we consider instead the one-year high-energy ($>$ 100 GeV) through-going muon sample in IceCube to set limits on new interactions in the $\mu\tau$-sector. Taking into account several sources of systematic errors, we obtain the bound $-6.0 \times 10^{-3} < \varepsilon_{\mu \tau} < 5.4 \times 10^{-3}$ at 90\% credible interval.
We also provide a forecast of the future sensitivity to $\varepsilon_{\mu \tau}$ by simulating 10~years of high-energy neutrino data in IceCube, and we find that if it is close to its current limit, IceCube high-energy atmospheric neutrino data can determine its value at high confidence.