The top-quark Yukawa coupling is extracted from the distribution of the top-quark pair () invariant mass in proton-proton collisions using 140 fb⁻¹ of data at √s = 13 TeV collected in 2015–2018 by the ATLAS experiment at the Large Hadron Collider. In the region near the production threshold, the invariant mass spectrum is sensitive to electroweak virtual corrections, including contributions from Higgs boson exchange, thereby providing sensitivity to the top-quark Yukawa coupling. This is the first measurement in ATLAS that aims to obtain this coupling exploiting this approach. The system is reconstructed in the single-lepton final state, requiring exactly one isolated electron or muon and at least four jets with at least two identified as originating from b-quarks. The measured Yukawa coupling is found to be in good agreement with the Standard Model prediction. An upper limit on the top-quark Yukawa coupling strength of Y_t < 2.1 relative to the Standard Model prediction is observed at 95% confidence level, consistent with the expected sensitivity.