We introduce an iterative solution to the problem of interference alignment (IA) over MIMO channels based on a message-passing formulation. We propose a parameterization of the messages that enables the computation of IA precoders by a min-sum algorithm over continuous variable spaces -- under this parameterization, suitable approximations of the messages can be computed in closed-form. We show that the iterative leakage minimization algorithm of Cadambe et al. is a special case of our message-passing algorithm, obtained for a particular schedule. Finally, we show that the proposed algorithm compares favorably to iterative leakage minimization in terms of convergence speed, and discuss a distributed implementation.