A measurement of single top-quark production in the s-channel is performed in proton–proton collisions at a centre-of-mass energy of 13 TeV with the ATLAS detector at the CERN Large Hadron Collider. The dataset corresponds to an integrated luminosity of 139 fb$^{−1}$. The analysis is performed on events with an electron or muon, missing transverse momentum and exactly two b-tagged jets in the final state. A discriminant based on matrix element calculations is used to separate single-top-quark s-channel events from the main background contributions, which are top-quark pair production and W-boson production in association with jets. The observed (expected) signal significance over the background-only hypothesis is 3.3 (3.9) standard deviations, and the measured cross-section is $ \sigma ={8.2}_{-2.9}^{+3.5} $ pb, consistent with the Standard Model prediction of $ {\sigma}^{\textrm{SM}}={10.32}_{-0.36}^{+0.40} $ pb.