A search for the rare decay D0→μ+μ− is reported using proton-proton collision events at 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 D0 mesons obtained from D*+→D0π+ decays. No significant excess is observed. A limit on the branching fraction of B(D0→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.