A search for direct production of low-mass dimuon resonances is performed using √s = 13 TeV proton-proton collision data collected by the CMS experiment during the 2017–2018 operation of the CERN LHC with an integrated luminosity of 96.6 fb⁻¹. The search exploits a dedicated high-rate trigger stream that records events with two muons with transverse momenta as low as 3 GeV but does not include the full event information. The search is performed by looking for narrow peaks in the dimuon mass spectrum in the ranges of 1.1–2.6 GeV and 4.2–7.9 GeV. No significant excess of events above the expectation from the standard model background is observed. Model-independent limits on production rates of dimuon resonances within the experimental fiducial acceptance are set. Competitive or world’s best limits are set at 90% confidence level for a minimal dark photon model and for a scenario with two Higgs doublets and an extra complex scalar singlet (2HDM+S). Values of the squared kinetic mixing coefficient ε² in the dark photon model above 10⁻⁶ are excluded over most of the mass range of the search. In the 2HDM+S, values of the mixing angle sin(θ_H) above 0.08 are excluded over most of the mass range of the search with a fixed ratio of the Higgs doublets vacuum expectation tan β = 0.5.