Message passing algorithms have been tailored for compressive imaging applications by plugging in different types of off-the-shelf image denoisers. These off-the-shelf denoisers mostly rely on some generic or hand-crafted priors for denoising. Due to their insufficient accuracy in capturing the true image prior, these methods often fail to produce satisfactory results, especially in highly underdetermined scenarios. On the other hand, score-based generative modeling offers a promising way to accurately characterize the sophisticated image distribution. In this paper, by exploiting the close relation between score-based modeling and empirical Bayes-optimal denoising, we devise a message passing framework that integrates a score-based minimum mean squared error (MMSE) denoiser for compressive image recovery. Experiments on the FFHQ dataset demonstrate that our method strikes a significantly better performance-complexity tradeoff than conventional message passing, regularized linear regression, and score-based posterior sampling baselines. Remarkably, our method typically converges in fewer than 20 neural function evaluations (NFEs).