The inclusive J /ψ nuclear modification factor (R AA ) in Pb–Pb collisions at s NN = 2.76 TeV has been measured by ALICE as a function of centrality in the e+ e− decay channel at mid-rapidity (|y| <0.8) and as a function of centrality, transverse momentum and rapidity in the μ + μ − decay channel at forward-rapidity (2.5 <y <4). The J /ψ yields measured in Pb–Pb are suppressed compared to those in pp collisions scaled by the number of binary collisions. The R AA integrated over a centrality range corresponding to 90% of the inelastic Pb–Pb cross section is 0.72 ± 0.06 (stat.) ± 0.10 ( syst. ) at mid-rapidity and 0.58 ± 0.01 (stat.) ± 0.09 ( syst. ) at forward-rapidity. At low transverse momentum, significantly larger values of R AA are measured at forward-rapidity compared to measurements at lower energy. These features suggest that a contribution to the J /ψ yield originates from charm quark (re)combination in the deconfined partonic medium.