Jets containing a prompt J/ψ meson are studied in lead-lead collisions at a nucleon-nucleon center-ofmass energy of 5.02 TeV, using the CMS detector at the LHC. Jets are selected to be in the transverse momentum range of 30 < pT < 40 GeV. The J/ψ yield in these jets is evaluated as a function of the jet fragmentation variable z, the ratio of the J/ψ pT to the jet pT. The nuclear modification factor, RAA, is then derived by comparing the yield in lead-lead collisions to the corresponding expectation based on proton-proton data, at the same nucleon nucleon center-of-mass energy. The suppression of the J/ψ yield shows a dependence on z, indicating that the interaction of the J/ψ with the quark-gluon plasma formed in heavy ion collisions depends on the fragmentation that gives rise to the J/ψ meson. ISSN:0370-2693 ISSN:0031-9163 ISSN:1873-2445