By analyzing an e+e- annihilation 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 the branching fraction of the D0→ρ-μ+νμ decay for the first time. We obtain BD0→ρ-μ+νμ=(1.35±0.09stat±0.09syst)×10-3. Using the world average of BD0→ρ-e+νe, we find a branching fraction ratio of BD0→ρ-μ+νμ/BD0→ρ-e+νe=0.90±0.11, which agrees with the theoretical expectation of lepton flavor universality within the uncertainty. Combining the world average of BD+→ρ0μ+νμ and the lifetimes of D0(+), we obtain a partial decay width ratio of ΓD0→ρ-μ+νμ/(2ΓD+→ρ0μ+νμ)=0.71±0.14, which is consistent with the isospin symmetry expectation of unity within 2.1σ. For the reported values of BD0→ρ-μ+νμ/BD0→ρ-e+νe and ΓD0→ρ-μ+νμ/2ΓD+→ρ0μ+νμ, the uncertainty is the quadratic sum of the statistical and systematic uncertainties.