The top-quark mass is measured using top-quark decays producing an isolated lepton and J/ψ meson reconstructed in its μ⁺μ⁻ decay mode. The data sample was recorded with the ATLAS detector in proton-proton collisions at a centre-of-mass energy of s√=13 TeV during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb⁻¹. The measurement is based on the invariant mass m(ℓμ⁺μ⁻) of the system made of the isolated lepton ℓ from the W boson decay and the non-isolated μ⁺μ⁻ pair from a J/ψ decay of a b-hadron, exploiting its sensitivity to the top-quark mass. An unbinned maximum-likelihood fit to the m(ℓμ⁺μ⁻) distribution is performed to extract the top-quark mass. The top-quark mass is measured to be m_top = 172.17 ± 0.80 (stat) ± 0.81 (syst) ± 1.07 (recoil) GeV, with a total uncertainty of 1.56 GeV. The third uncertainty arises from changing the dipole parton shower gluon-recoil scheme used in top-quark decays.