Postacquisition denoising of magnetic resonance (MR) images is of importance for clinical diagnosis and computerized analysis, such as tissue classification and segmentation. It has been shown that the noise in MR magnitude images follows a Rician distribution, which is signal-dependent when signal-to-noise ratio (SNR) is low. It is particularly difficult to remove the random fluctuations and bias introduced by Rician noise. The objective of this paper is to estimate the noise free signal from MR magnitude images. We model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution. We propose a nonlocal maximum likelihood (NLML) estimation method for Rician noise reduction. Our method yields an optimal estimation result that is more accurate in recovering the true signal from Rician noise than NL means algorithm in the sense of SNR, contrast, and method error. We demonstrate that NLML performs better than the conventional local maximum likelihood (LML) estimation method in preserving and defining sharp tissue boundaries in terms of a well-defined sharpness metric while also having superior performance in method error.