Graphs are a natural representation of brain activity derived from functional magnetic imaging (fMRI) data. It is well known that communities of nodes extracted from brain graphs, referred to as functional connectivity networks (FCNs), serve as useful biomarkers for understanding brain function and dysfunction. Previous works, however, ignore the temporal dynamics of the brain and focus on static graph representations. In this paper we propose DBGDGM, a dynamic brain graph deep generative model which simultaneously learns graph-, node-, and community-level embeddings in an unsupervised fashion. Specifically, DBGDGM represents brain graph nodes as embeddings sampled from a distribution over communities that evolve over time. The community distribution is parameterized using neural networks that learn from subject and node embed- dings as well as past community assignments. Experiments on real-world fMRI data demonstrate DBGDGM outperforms state-of-the-art baselines in graph generation, dynamic link prediction, and is comparable for graph classification. Finally, an interpretability analysis of the learnt community distributions reveals overlap with known FCNs reported in neuroscience literature.