The ALICE collaboration performed the first rapidity-differential measurement of coherent J/ψ photoproduction in ultra-peripheral Pb–Pb collisions at a center-of-mass energy s_NN=5.02 TeV. The J/ψ is detected via its dimuon decay in the forward rapidity region (−4.0<y<−2.5) for events where the hadronic activity is required to be minimal. The analysis is based on an event sample corresponding to an integrated luminosity of about 750 μb⁻¹. The cross section for coherent J/ψ production is presented in six rapidity bins. The results are compared with theoretical models for coherent J/ψ photoproduction. These comparisons indicate that gluon shadowing effects play a role in the photoproduction process. The ratio of ψ^′ to J/ψ coherent photoproduction cross sections was measured and found to be consistent with that measured for photoproduction off protons.