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...