A bstract The transverse momentum ( p T ) and centrality dependence of the nuclear modification factor R AA of prompt and non-prompt J/ ψ , the latter originating from the weak decays of beauty hadrons, have been measured by the ALICE collaboration in Pb–Pb collisions at s NN = 5.02 TeV. The measurements are carried out through the e + e − decay channel at midrapidity (| y | < 0.9) in the transverse momentum region 1.5 < p T < 10 GeV/ c . Both prompt and non-prompt J/ ψ measurements indicate a significant suppression for p T > 5 GeV/ c , which becomes stronger with increasing collision centrality. The results are consistent with similar LHC measurements in the overlapping p T intervals, and cover the kinematic region down to p T = 1.5 GeV/ c at midrapidity, not accessible by other LHC experiments. The suppression of prompt J/ ψ in central and semicentral collisions exhibits a decreasing trend towards lower transverse momentum, described within uncertainties by models implementing J/ ψ production from recombination of c and c ¯ quarks produced independently in different partonic scatterings. At high transverse momentum, transport models including quarkonium dissociation are able to describe the suppression for prompt J/ ψ . For non-prompt J/ ψ , the suppression predicted by models including both collisional and radiative processes for the computation of the beauty-quark energy loss inside the quark-gluon plasma is consistent with measurements within uncertainties.