The production of exclusive gamma gamma -> mu(+)mu(-) 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 12 GeV < m(mu+mu-) < 70 GeV. 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. (c) 2017 The Author(s). Published by Elsevier B.V.