Abstract: Non-standard interactions in the propagation of neutrinos in matter can lead to significant deviations from expectations within the standard neutrino oscillation framework and atmospheric neutrino detectors have been considered to set constraints. However, most previous works have focused on relatively low-energy atmospheric neutrino data. Here, we consider the one-year high-energy through-going muon data in IceCube, which has been already used to search for light sterile neutrinos, to constrain new interactions in the μtau-sector. In our analysis we include several systematic uncertainties on both, the atmospheric neutrino flux and on the detector properties, which are accounted for via nuisance parameters. After considering different primary cosmic-ray spectra and hadronic interaction models, we improve over previous analysis by using the latest data and showing that systematics currently affect very little the bound on the off-diagonal epsilon(mu tau), with the 90% credible interval given by -6.0 x 10(-3) < epsilon(mu tau) < 5.4 x 10(-3), comparable to previous results. In addition, we also estimate the expected sensitivity after 10 years of collected data in IceCube and study the precision at which non-standard parameters could be determined for the case of epsilon(mu tau) near its current bound.