We report on a search for the pair production of second generation scalar leptoquarks (LQ) in ppbar collisions at the center of mass energy sqrt(s)=1.96 TeV using a data set corresponding to an integrated luminosity of 1.0 fb-1 collected with the D0 experiment at the Fermilab Tevatron Collider. Topologies arising from the LQLQbar->muqnuq and LQLQbar->muqmuq decay modes are investigated. No excess of data over the standard model prediction is observed and upper limits on the leptoquark pair production cross section are derived at the 95% C.L. as a function of the leptoquark mass and the branching fraction beta for the decay LQ->muq. These are interpreted as lower limits on the leptoquark mass as a function of beta. For beta=1 (0.5), scalar second generation leptoquarks with masses up to 316 GeV (270 GeV) are excluded.