Rician noise contaminated Magnetic Resonance (MR) Images can effect the accuracy of quantitative analysis. For accurate analysis of MR data, noise smoothing is considered as an important pre-processing step. In this article, a novel Fuzzy Similarity based Non-Local Means (FSNLM) filter has been proposed for the removal of Rician noise from MR images. Proposed technique consists of three major modules: Pre-processing, Fuzzy similarity and Fuzzy restoration. In pre-processing module, some important statistical parameters are identified. These parameters are then used by the fuzzy similarity mechanism to find non-local homogeneous neighboring pixels. Selected homogeneous pixels play an important role during fuzzy logic based restoration process for the estimation of noise-free pixels. The proposed scheme FSNLM has been tested on simulated and real data sets, and compared with state-of-the-art filters based on well known global and local quantitative measures such as root-mean-squared-error (RMSE), peak-signal-to-noise-ratio (PSNR), structural-similarity-index-measure (SSIM), and figure-of-merit (FOM). Experimental results show that the proposed noise filtering technique is more effective than the existing methods, both at low and high densities of Rician noise.