This document describes the search for second-generation leptoquarks (LQ_2) in around 114 pb^-1 of proton-antiproton collisions, recorded with the D0 detector between September 2002 and June 2003 at a centre-of-mass energy of sqrt{s} = 1.96 TeV. The predictions of the Standard Model and models including scalar leptoquark production are compared to the data for various kinematic distributions. Since no excess of data over the Standard Model prediction has been observed, a lower limit on the leptoquark mass of M(LQ_2)_{beta=1} > 200 GeV/c^2 has been calculated at 95% confidence level (C.L.), assuming a branching fraction of beta = BF(LQ_2 --> mu j) = 100% into a charged lepton and a quark. The corresponding limit for beta = 1/2 is M(LQ_2)_{beta=1/2} > 152 GeV/c^2. Finally, the results were combined with those from the search in the same channel at D0 Run I. This combination yields the exclusion limit of 222 GeV/c^2 (177 GeV/c^2) for beta=1 (1/2) at 95% C.L., which is the best exclusion limit for scalar second-generation leptoquarks (for beta=1) from a single experiment to date.