The ALICE experiment has measured the inclusive J/ψ production in Pb-Pb collisions at √s(NN) = 2.76 TeV down to zero transverse momentum in the rapidity range 2.5 < y < 4. A suppression of the inclusive J/ψ yield in Pb-Pb is observed with respect to the one measured in pp collisions scaled by the number of binary nucleon-nucleon collisions. The nuclear modification factor, integrated over the 0%-80% most central collisions, is 0.545 ± 0.032(stat) ± 0.083(syst) and does not exhibit a significant dependence on the collision centrality. These features appear significantly different from measurements at lower collision energies. Models including J/ψ production from charm quarks in a deconfined partonic phase can describe our data.