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 $1.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected in $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ 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 $\ensuremath{\sigma}\ifmmode\times\else\texttimes\fi{}\mathcal{B}(pp\ensuremath{\rightarrow}a\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$ in the range of 1.5--7.5 pb. These results improve on existing bounds on the $ab\overline{b}$ coupling for ${m}_{a}<{m}_{\ensuremath{\Upsilon}(1S)}$ and are the first significant limits for ${m}_{a}>{m}_{\ensuremath{\Upsilon}(3S)}$. Constraints on the supersymmetric parameter space are presented in the context of the next-to-minimal model.