A search for the rare decay D^{0}→μ^{+}μ^{-} is reported using proton-proton collision events at sqrt[s]=13.6 TeV collected by the CMS detector in 2022-2023, corresponding to an integrated luminosity of 64.5 fb^{-1}. This is the first analysis to use a newly developed inclusive dimuon trigger, expanding the scope of the CMS flavor physics program. The search uses D^{0} mesons obtained from D^{*+}→D^{0}π^{+} decays. No significant excess is observed. A limit on the branching fraction of B(D^{0}→μ^{+}μ^{-})<2.4×10^{-9} at 95% confidence level is set. This is the most stringent upper limit set on any flavor changing neutral current decay in the charm sector.