Let F/\mathbb{Q} be a totally real extension and f an Hilbert modular cusp form of level \mathfrak{n} , with trivial central character and parallel weight 2, which is an eigenform for the action of the Hecke algebra. Fix a prime \wp | \mathfrak{n} of F of residual characteristic p . Let K/F be a quadratic totally imaginary extension and K_{\wp^\infty} be the \wp -anticyclotomic \mathbb{Z}_p -extension of K . The main result of this paper, generalizing the analogous result [5] of Bertolini and Darmon, states that, under suitable arithmetic assumptions and some technical restrictions, the characteristic power series of the Pontryagin dual of the Selmer group attached to (f,K_{\wp^\infty}) divides the p -adic L -function attached to (f,K_{\wp^\infty}) , thus proving one direction of the Anticyclotomic Main Conjecture for Hilbert modular forms. Arithmetic applications are given.