A measurement of the exclusive two-photon production of muon pairs in proton-proton collisions at root s = 7 TeV, pp -> p mu(+)mu(-) p, is reported using data corresponding to an integrated luminosity of 40 pb-1. For muon pairs with invariant mass greater than 11.5 GeV, transverse momentum p(T)(mu) > 4 GeV and pseudorapidity 1770.1) < 2.1, a fit to the dimuon p(T)(mu(+)mu(-)) distribution results in a measured cross section of sigma(p -> p mu(+)mu(-) p) - 3.38(-0.55)(+0.58) (stat.)+/- 0.16 (syst.) +/- 0.14 (lumi.) pb, consistent with the theoretical prediction evaluated with the event generator LPAIR. The ratio to the predicted cross section is 0.83+(0.14)(-0.13) (stat.) +/- 0.04 (syst.) +/- 0.03 (lumi.). The characteristic distributions of the muon pairs produced via Ty fusion, such as the muon acoplanarity, the muon pair invariant mass and transverse momentum agree with those from the theory.