The dimuon invariant mass spectrum is searched in the range between 5.5 and 14GeV 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 1.3fb-1 collected in pp collisions at √s=7TeV 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 σ×B(pp→a→μ+μ-) in the range of 1.5-7.5pb. These results improve on existing bounds on the abb̄ coupling for ma<mΥ(1S) and are the first significant limits for ma>mΥ(3S). Constraints on the supersymmetric parameter space are presented in the context of the next-to-minimal model. © 2012 CERN. Published by the American Physical Society under the terms of the http://creativecommons.org/licenses/by/3.0/ Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.