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We report the first observation of the semimuonic decay 𝐷+→𝜔𝜇+𝜈𝜇 using an 𝑒+𝑒− collision data sample corresponding to an integrated luminosity of 2.93 fb−1 collected with the BESIII detector at a center-of-mass energy of 3.773 GeV. The absolute branching fraction of the 𝐷+→𝜔𝜇+𝜈𝜇 decay is measured to be ℬ𝐷+→𝜔𝜇+𝜈𝜇=(17.7±1.8stat±1.1syst)×10−4. Its ratio with the world average value of the branching fraction of the 𝐷+→𝜔𝑒+𝜈𝑒 decay probes lepton flavor universality and it is determined to be ℬ𝐷+→𝜔𝜇+𝜈𝜇/ℬPDG 𝐷+→𝜔𝑒+𝜈𝑒=1.05±0.14, in agreement with the standard model expectation within one standard deviation.