The results of a search for the production of second generation scalar leptoquarks are presented for final states consisting of either two muons and at least two jets or a muon plus missing transverse momentum and at least two jets. A total of 1.03 fb(-1) integrated luminosity of proton-proton collision data produced by the Large Hadron Collider at root s = 7 TeV and recorded by the ATLAS detector is used for the search. The event yields in the signal regions are found to be consistent with the Standard Model background expectations. The production of second generation leptoquarks is excluded for a leptoquark mass m(LQ) < 594 (685) GeV at 95 % confidence level, for a branching ratio of 0.5 (1.0) for leptoquark decay to a muon and a quark.