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 similar to 16 GeV to 100 GeV, have been analysed. A log-likelihood ratio test of the dimensionless coefficients epsilon(mu tau) and epsilon(tau tau) – epsilon(mu mu) does not provide clear evidence of deviations from standard interactions. For normal neutrino mass ordering, the combined fit of both coefficients yields a value 1.7 sigma away from the null result. However, the 68% and 95% confidence level intervals for epsilon(mu tau) and epsilon(tau tau) – epsilon(mu mu), 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 epsilon(mu tau) is among the most stringent to date and it further restrains the strength of possible non-standard interactions in the μ- tau sector.