Channel estimation is a critical task in digital communications that greatly impacts end-to-end system performance. In this work, we introduce a novel approach for multiple-input multiple-output (MIMO) channel estimation using score-based generative models. Our method uses a deep neural network that is trained to estimate the gradient of the log-prior of wireless channels at any point in high-dimensional space, and leverages this model to solve channel estimation via posterior sampling. We train a score-based model on channel realizations from the CDL-D model for two antenna spacings and show that the approach leads to competitive in- and out-of-distribution performance when compared to generative adversarial network (GAN) and compressed sensing (CS) methods. When tested on CDL-D channels, the approach leads to a gain of at least $5$ dB in channel estimation error compared to GAN methods in-distribution at $λ/2$ antenna spacing. When tested on CDL-C channels which are never seen during training or fine-tuned on, the approach leads to end-to-end coded performance gains of up to $3$ dB compared to CS methods and losses of only $0.5$ dB compared to ideal channel knowledge.