A measurement of the Drell-Yan transverse momentum (p_Tμμ) distribution above the Z-boson mass region (116 GeV < M_μμ) in proton-proton collisions at a center-of-mass energy of 7 TeV is presented. Results are obtained using Z/γ* → μ+μ- decays in a data sample collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 36 pb-1. The normalized differential cross-section is measured up to p_Tμμ of 180 GeV. We measure the ratio of the p_Tμμ distribution in the high mass region to that in the Z-boson mass region and multiply it with the high-statistics p_Tμμ distribution in the Z-mass region. Both experimental and theoretical uncertainties cancel largely in the cross-section ratio. The results are compared with predictions of perturbative QCD and event generators and are found to agree with the prediction of resummed QCD combined with fixed-order perturbative QCD over the full p_Tμμ range.