Abstract : The dimuon invariant mass spectrum is searched in the range between 5.5 and 14 GeV for a light pseudoscalar Higgs boson "a", predicted in a number of new physics models, including the next-to-minimal supersymmetric standard model. The data sample used in the search corresponds to an integrated luminosity of 1.3 inverse femtobarns collected in pp collisions at sqrt(s) = 7 TeV with the CMS detector at the LHC. No excess is observed above the background predictions and upper limits are set on the cross section times branching fraction sigma times B(pp to "a" to an oppositely charged muon pair) in the range of 1.5-7.5 pb. These results improve on existing bounds on the "a" b-bbar coupling for m("a") < m(Upsilon(1S)) and are the first significant limits for m("a") > m(Upsilon(1S)). Constraints on the supersymmetric parameter space are presented in the context of the next-to-minimal model.