We propose Neural Cellular Automata (NCA) to simulate the microstructure development during the solidification process in metals. Based on convolutional neural networks, NCA can learn essential solidification features, such as preferred growth direction and competitive grain growth, and are up to six orders of magnitude faster than the conventional Cellular Automata (CA). Notably, NCA deliver reliable predictions also outside their training range, e.g. for larger domains, longer solidification duration, and different temperature fields and nucleation settings, which indicates that they learn the physics of the solidification process. While in this study we employ data produced by CA for training, NCA can be trained based on any microstructural simulation data, e.g. from phase-field models.