Inclusive J/$\psi$ production has been studied with the ALICE detector in p-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV at the CERN LHC, in the rapidity domains 2.03 < y$_{cms}$ < 3.53 and −4.46 < y$_{cms}$ < −2.96, down to zero transverse momentum. The J/$\psi$ measurement is performed in the Muon Spectrometer through the $\mu^+\mu^−$ decay mode. In this Letter, the J/$\psi$ production cross section and the nuclear modification factor R$_{pPb}$ for the rapidities under study are presented. While at forward rapidity a suppression of the J/$\psi$ 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 shown differentially in rapidity...