A search for contact interactions has been performed using dimuon events recorded with the ATLAS detector in proton-proton collisions at sqrt(s) = 7 TeV. The data sample corresponds to an integrated luminosity of 42 pb-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: Lambda > 4.9 TeV (4.5 TeV) for constructive (destructive) interference in the left-left isoscalar compositeness model. These limits are the most stringent to date for mumuqq contact interactions.