A cell's shape and motion represent fundamental aspects of cell identity and can be highly predictive of function and pathology. However, automated analysis of the morphodynamic states remains challenging for most cell types, especially primary human cells where genetic labeling may not be feasible. To enable automated and quantitative analysis of morphodynamic states, we developed DynaMorph-a computational framework that combines quantitative live cell imaging with self-supervised learning. To demonstrate the robustness and utility of this approach, we used DynaMorph to annotate morphodynamic states observed with label-free measurements of optical density and anisotropy of live microglia isolated from human brain tissue. These cells show complex behavior and have varied responses to disease-relevant perturbations. DynaMorph generates quantitative morphodynamic representations that can be used to compare the effects of the perturbations. Using DynaMorph, we identify distinct morphodynamic states of microglia polarization and detect rare transition events between states. The concepts and the methods presented here can facilitate automated discovery of functional states of diverse cellular systems.