The production of exclusive γγ→μ+μ− events in proton–proton collisions at a centre-of-mass energy of 13 TeV is measured with the ATLAS detector at the LHC, using data corresponding to an integrated luminosity of 3.2 fb−1. The measurement is performed for a dimuon invariant mass of 12GeV<mμ+μ−<70GeV. The integrated cross-section is determined within a fiducial acceptance region of the ATLAS detector and differential cross-sections are measured as a function of the dimuon invariant mass. The results are compared to theoretical predictions both with and without corrections for absorptive effects.