By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb-1 collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure for the first time the absolute branching fraction of the D+→ημ+νμ decay to be BD+→ημ+νμ=(10.4±1.0stat±0.5syst)×10-4. Using the world averaged value of BD+→ηe+νe, the ratio of the two branching fractions is determined to be BD+→ημ+νμ/BD+→ηe+νe=0.91±0.13(stat+syst), which agrees with the theoretical expectation of lepton flavor universality within uncertainty. By studying the differential decay rates in five four-momentum transfer intervals, we obtain the product of the hadronic form factor f+η(0) and the c→d Cabibbo-Kobayashi-Maskawa matrix element |Vcd| to be f+η(0)|Vcd|=0.087±0.008stat±0.002syst. Taking the input of |Vcd| from the global fit in the standard model, we determine f+η(0)=0.39±0.04stat±0.01syst. On the other hand, using the value of f+η(0) calculated in theory, we find |Vcd|=0.242±0.022stat±0.006syst±0.033theory.