Abstract Non-standard interactions of neutrinos arising in many theories beyond the Standard Model can significantly alter matter effects in atmospheric neutrino propagation through the Earth. In this paper, a search for deviations from the prediction of the standard 3-flavour atmospheric neutrino oscillations using the data taken by the ANTARES neutrino telescope is presented. Ten years of atmospheric neutrino data collected from 2007 to 2016, with reconstructed energies in the range from ∼16 GeV to 100 GeV, have been analysed. A log-likelihood ratio test of the dimensionless coefficients ε_μτ and ε_ττ − ε_μμ does not provide clear evidence of deviations from standard interactions. For normal neutrino mass ordering, the combined fit of both coefficients yields a value 1.7σ away from the null result. However, the 68% and 95% confidence level intervals for ε_μτ and ε_ττ − ε_μμ, respectively, contain the null value. Best fit values, one standard deviation errors and bounds at the 90% confidence level for these coefficients are given for both normal and inverted mass orderings. The constraint on ε_μτ is among the most stringent to date and it further restrains the strength of possible non-standard interactions in the μ − τ sector.