A search for neutral Higgs bosons predicted in the minimal supersymmetric standard model (MSSM) for μ+μ− decay channels is presented. The analysis uses data collected by the CMS experiment at the LHC in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.3 fb−1, respectively. The search is sensitive to Higgs bosons produced either through the gluon fusion process or in association with a bb‾ quark pair. No statistically significant excess is observed in the μ+μ− mass spectrum. Results are interpreted in the framework of several benchmark scenarios, and the data are used to set an upper limit on the MSSM parameter tan⁡β as a function of the mass of the pseudoscalar A boson in the range from 115 to 300 GeV. Model independent upper limits are given for the product of the cross section and branching fraction for gluon fusion and b quark associated production at s=8 TeV. They are the most stringent limits obtained to date in this channel.