We report the first observation of the semi-muonic decay $D^+to omega mu^+ u_mu$ using an $e^+e^-$ collision data sample corresponding to an integrated luminosity of $2.93~mathrm{fb}^{-1}$ collected with the BESIII detector at a center-of-mass energy of 3.773 GeV. The absolute branching fraction of the $D^+to omega mu^+ u_mu$ decay is measured to be ${mathcal B}_{D^+to omegamu^+ u_mu}=(17.7pm1.8_{rm stat}pm1.1_{rm syst})times 10^{-4}$. Its ratio with the world average value of the branching fraction of the $D^+to omega e^+ u_e$ decay probes lepton flavor universality and it is determined to be ${mathcal B}_{D^+to omega mu^+ u_mu}/{mathcal B}^{rm PDG}_{D^+to omega e^+ u_e}=1.05pm0.14$, in agreement with the standard model expectation within one standard deviation.
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