The fragmentation of jets containing a J/ψ meson is studied in pp data using an integrated luminosity of . The fraction of the jet transverse momentum pT,jet carried by the J/ψ is measured for prompt J/ψ and J/ψ coming from b hadron decays, named nonprompt. Whereas the fragmentation function of nonprompt J/ψ is well-modeled by simulations using a Monte Carlo generator, the prompt J/ψ are found to be accompanied by a larger level of jet activity. The fraction of J/ψ mesons that are produced inside a jet is also reported, and found to be larger in data than in simulation, for both prompt and nonprompt J/ψ.