Models of Virtual Cells and Virtual Tissues at single-cell resolution would allow us to test perturbations in silico and accelerate progress in tissue and cell engineering. However, most such models are not rooted in causal inference and as a result, could mistake correlation for causation. We introduce Celcomen, a novel generative graph neural network grounded in mathematical causality to disentangle intra- and inter-cellular gene regulation in spatial transcriptomics and single-cell data. Celcomen can also be prompted by perturbations to generate spatial counterfactuals, thus offering insights into experimentally inaccessible states, with potential applications in human health. We validate the model's disentanglement and identifiability through simulations, and demonstrate its counterfactual predictions in clinically relevant settings, including human glioblastoma and fetal spleen, recovering inflammation-related gene programs post immune system perturbation. Moreover, it supports mechanistic interpretability, as its parameters can be reverse-engineered from observed behavior, making it an accessible model for understanding both neural networks and complex biological systems.