Atmospheric neutrinos provide a unique avenue to study neutrino interactions in matter. In this work, the prospects of constraining non-standard neutrino interactions with atmospheric neutrino oscillations are investigated for the proposed ESSnuSB far detector. By analyzing atmospheric neutrino samples equivalent to 5.4 Mt·year exposure, it is found that ESSnuSB could be able to set the upper bounds ∣ϵeμm∣<0.053,∣ϵeτm∣<0.057,∣ϵμτm∣<0.021,ϵeem−ϵμμm<0.075 and ∣ϵττm−ϵμμm∣<0.031 at 90% CL, when the results are minimized for ϕeμm,ϕeτm and ϕμτm and normal ordering is assumed for neutrino masses. It is also shown that the presence of non-standard interactions could affect the sensitivities to neutrino mass ordering and θ23 octant in comparison to the standard interaction scheme. The results of this work highlight the complementarity between atmospheric and accelerator neutrino programs in ESSnuSB.