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 fb(-1) collected in pp collisions at root 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 x B(pp -> a -> mu(+) mu(-)) in the range of 1.5-7.5 pb. These results improve on existing bounds on the ab (b) over bar coupling for m(a) < m(gamma(1s)) and are the first significant limits for m(a) > m(gamma(3S)). Constraints on the supersymmetric parameter space are presented in the context of the next-to-minimal model.