Magnetic Resonance Imaging (MRI) is one of the most important techniques in medical imaging and Rician noise is a common noise that naturally appears in MRI images. Low rank matrix approximation approaches have been widely used in image processing such as image denoising, which takes advantage of the idea of nonlocal self-similarity between patches in a natural image. The weighted nuclear norm minimization method as a low rank matrix approximation approach has shown to be an effective approach for image denoising. Inspired by this, we propose in this paper a MAP model with the weighted nuclear norm as a regularization constraint to remove Rician noise. The MAP data fidelity term has a Lipschitz continuous gradient and the weighted nuclear norm can be efficiently minimized. We propose an iterative weighted nuclear norm minimization algorithm (IWNNM) to solve the proposed non-convex model and analyze the convergence of our algorithm. The computational results show that our proposed method is promising in restoring images corrupted with Rician noise.