A nonlocal minimum mean square error (MMSE) image denoising algorithm to remove Poisson noise is proposed in this work. Based on the Bayesian estimation theory, we first derive the nonlocal MMSE denoising filter, which can minimize the mean square error (MSE) of a denoised block. Then, we develop an approximation of the filter for practical implementation. Simulation results show that the proposed algorithm provides significantly better denoising performance than the conventional nonlocal means filter and its recent extension for Poisson noise.