Results are reported from a search for the effects of contact interactions using events with a high-mass, oppositely charged muon pair. The events are collected in proton-proton collisions at s√=7 TeV using the Compact Muon Solenoid detector at the Large Hadron Collider. The data sample corresponds to an integrated luminosity of 5.3 fb−1. The observed dimuon mass spectrum is consistent with that expected from the standard model. The data are interpreted in the context of a quark- and muon-compositeness model with a left-handed isoscalar current and an energy scale parameter Λ. The 95% confidence level lower limit on Λ is 9.5 TeV under the assumption of destructive interference between the standard model and contact-interaction amplitudes. For constructive interference, the limit is 13.1 TeV. These limits are comparable to the most stringent ones reported to date.