Inclusive J/ ? production has been studied with the ALICE detector in p-Pb collisions at the nucleon-nucleon center of mass energy v sNN = 5.02 TeV at the CERN LHC. The measurement is performed in the center of mass rapidity domains 2 .03 < ycms < 3 .53 and - 4 .46 < ycms < - 2 .96, down to zero transverse momentum, studying the µ + µ - decay mode. In this paper, the J/ ? production cross section and the nuclear modification factor RpPb for the rapidities under study are presented. While at forward rapidity, corresponding to the proton direction, a suppression of the J/ ? yield with respect to binary-scaled pp collisions is observed, in the backward region no suppression is present. The ratio of the forward and backward yields is also measured di fferentially in rapidity and transverse momentum. Theoretical predictions based on nuclear shadowing, as well as on models including, in addition, a contribution from partonic energy loss, are in fair agreement with the experimental results.