We study the spin-dependent transmission through a potential barrier in a zigzag graphene nanoribbon. In particular, we consider the effect of the magnetic order of the ribbon induced by the modulation of the local density introduced by the barrier. We model the system using an Anderson–Hubbard model that we treat in the mean field approximation. We solve this problem self-consistently and calculate the transmission coefficient using the recursive Green function method. We find that Fano-like interference dips appear on one of the spin channels as the result of the presence of spin polarized edge states in the barrier.