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We report the first measurement of the semileptonic decay Ds+→K0μ+νμ, using a sample of e+e- annihilation data corresponding to an integrated luminosity of 7.33 fb-1 collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fraction of the decay is measured to be B(Ds+→K0μ+νμ)=(2.89±0.27stat±0.12syst)×10-3, where the first uncertainty is statistical and the second is systematic. Based on a simultaneous fit to the partial decay rates in q2 intervals measured in Ds+→K0μ+νμ and Ds+→K0e+νe decays, the product value of the form factor f+K0(0) and the Cabibbo-Kobayashi-Maskawa matrix element |Vcd| is measured to be f+K0(0)|Vcd|=0.140±0.008stat±0.003syst, which is the most precise determination to date. In addition, lepton flavor universality is tested for the first time with Ds+→K0ℓ+νℓ decays in full and separate q2 intervals. No violation is found.