This Letter presents a measurement of γγ→μ^{+}μ^{-} production in Pb+Pb collisions recorded by the ATLAS detector at the Large Hadron Collider at sqrt[s_{NN}]=5.02 TeV with an integrated luminosity of 0.49 nb^{-1}. The azimuthal angle and transverse momentum correlations between the muons are measured as a function of collision centrality. The muon pairs are produced from γγ through the interaction of the large electromagnetic fields of the nuclei. The contribution from background sources of muon pairs is removed using a template fit method. In peripheral collisions, the muons exhibit a strong back-to-back correlation consistent with previous measurements of muon pair production in ultraperipheral collisions. The angular correlations are observed to broaden significantly in central collisions. The modifications are qualitatively consistent with rescattering of the muons while passing through the hot matter produced in the collision.