A search for the dimuon decay of the Standard Model (SM) Higgs boson is performed using data corresponding to an integrated luminosity of 139 fb(-1) collected with the ATLAS detector in Run 2 pp collisions at root s = 13 TeV at the Large Hadron Collider. The observed (expected) significance over the background-only hypothesis for a Higgs boson with a mass of 125.09 GeV is 2.0 sigma (1.7 sigma). The observed upper limit on the cross section times branching ratio for pp -> H -> mu mu is 2.2 times the SM prediction at 95% confidence level, while the expected limit on a H -> mu mu signal assuming the absence (presence) of a SM signal is 1.1(2.0). The best-fit value of the signal strength parameter, defined as the ratio of the observed signal yield to the one expected in the SM, is mu = 1.2 +/- 0.6.