Neutral-current production of K+ by atmospheric neutrinos is a background in searches for the proton decay p→K+ν. Reactions such as νp→νK+Λ are indistinguishable from proton decays when the decay products of the Λ are below detection threshold. Events with K+ are identified in MINERvA by reconstructing the timing signature of a K+ decay at rest. A sample of 201 neutrino-induced neutral-current K+ events is used to measure differential cross sections with respect to the K+ kinetic energy, and the non-K+ hadronic visible energy. An excess of events at low hadronic visible energy is observed relative to the prediction of the neut event generator. Good agreement is observed with the cross section prediction of the genie generator. A search for photons from π0 decay, which would veto a neutral-current K+ event in a proton decay search, is performed, and a 2σ deficit of detached photons is observed relative to the genie prediction.