© 2018 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 . As atmospheric neutrinos propagate through the Earth, vacuumlike oscillations are modified by Standard Model neutral- and charged-current interactions with electrons. Theories beyond the Standard Model introduce heavy, TeV-scale bosons that can produce nonstandard neutrino interactions. These additional interactions may modify the Standard Model matter effect producing a measurable deviation from the prediction for atmospheric neutrino oscillations. The result described in this paper constrains nonstandard interaction parameters, building upon a previous analysis of atmospheric muon-neutrino disappearance with three years of IceCube DeepCore data. The best fit for the muon to tau flavor changing term is ϵμτ=-0.0005, with a 90% C.L. allowed range of -0.0067<ϵμτ<0.0081. This result is more restrictive than recent limits from other experiments for ϵμτ. Furthermore, our result is complementary to a recent constraint on ϵμτ using another publicly available IceCube high-energy event selection. Together, they constitute the world's best limits on nonstandard interactions in the μ-τ sector.