We report on a search for second generation leptoquarks LQ_2 which decay into a muon plus quark in p\bar{p} collisions at a center-of-mass energy of sqrt{s} = 1.96 TeV in the D0 detector using an integrated luminosity of about 300 pb-1. No evidence for a leptoquark signal is observed and an upper bound on the product of the cross section for single leptoquark production times branching fraction beta into a quark and a muon was determined for second generation scalar leptoquarks as a function of the leptoquark mass. This result has been combined with a previously published D0 search for leptoquark pair production to obtain leptoquark mass limits as a function of the leptoquark-muon-quark coupling, lambda. Assuming lambda=1, lower limits on the mass of a second generation scalar leptoquark are m{LQ_2}>274 GeV and m{LQ_2}>226 GeV for beta=1 and beta=1/2, respectively.