Production of K^{+} mesons in charged-current u_{mu} interactions on plastic scintillator (CH) is measured using MINERvA exposed to the low-energy NuMI beam at Fermilab. Timing information is used to isolate a sample of 885 charged-current events containing a stopping K^{+} which decays at rest. The differential cross section in K^{+} kinetic energy, dsigma/dT_{K}, is observed to be relatively flat between 0 and 500 MeV. Its shape is in good agreement with the prediction by the textsc{genie} neutrino event generator when final-state interactions are included, however the data rate is lower than the prediction by 15%.