A search for contact interactions has been performed using dimuon events recorded with the ATLAS detector in proton-proton collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$. The data sample corresponds to an integrated luminosity of $42\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. No significant deviation from the standard model is observed in the dimuon mass spectrum, allowing the following 95% C.L. limits to be set on the energy scale of contact interactions: $\ensuremath{\Lambda}>4.9\text{ }\text{ }\mathrm{TeV}$ (4.5 TeV) for constructive (destructive) interference in the left-left isoscalar compositeness model. These limits are the most stringent to date for $\ensuremath{\mu}\ensuremath{\mu}qq$ contact interactions.