The production of J/ψ mesons in jets is studied in the forward region of proton-proton collisions using data collected with the LHCb detector at a center-of-mass energy of 13 TeV. The fraction of the jet transverse momentum carried by the J/ψ meson, z(J/ψ)≡pT(J/ψ)/pT(jet), is measured using jets with pT(jet)>20 GeV in the pseudorapidity range 2.5<η(jet)<4.0. The observed z(J/ψ) distribution for J/ψ mesons produced in b-hadron decays is consistent with expectations. However, the results for prompt J/ψ production do not agree with predictions based on fixed-order nonrelativistic QCD. This is the first measurement of the pT fraction carried by prompt J/ψ mesons in jets at any experiment.Received 19 January 2017DOI:https://doi.org/10.1103/PhysRevLett.118.192001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2017 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasParticle productionQuantum chromodynamicsParticles & Fields