A search for pair production of second-generation scalar leptoquarks in the final state with two muons and two jets is performed using proton-proton collision data at root s = 7 TeV collected by the CMS detector at the LHC. The data sample used corresponds to an integrated luminosity of 34 pb(-1). The number of observed events is in good agreement with the predictions from the standard model processes. An upper limit is set on the second-generation leptoquark cross section times beta(2) as a function of the leptoquark mass, and leptoquarks with masses below 394 GeV are excluded at a 95\% confidence level for beta = 1, where beta is the leptoquark branching fraction into a muon and a quark. These limits are the most stringent to date.