A transformation of the US electricity sector is underway with aggressive targets to achieve 100% carbon pollution-free electricity by 2035. To achieve this objective while maintaining a safe and reliable power grid, new operating paradigms are needed, of computationally fast and accurate decision making in a dynamic and uncertain environment. We propose a novel physics-informed machine learning framework for the decision of dynamic grid reconfiguration (PhML-DyR), a key task in power systems. Dynamic reconfiguration (DyR) is a process by which switch-states are dynamically set so as to lead to an optimal grid topology that minimizes line losses. To address the underlying computational complexities of NP-hardness due to the mixed nature of the decision variables, we propose the use of physics-informed ML (PhML) which integrates both operating constraints and topological and connectivity constraints into a neural network framework. Our PhML approach learns to simultaneously optimize grid topology and generator dispatch to meet loads, increase efficiency, and remain within safe operating limits. We demonstrate the effectiveness of PhML-DyR on a canonical grid, showing a reduction in electricity loss by 23%, and improved voltage profiles. We also show a reduction in constraint violations by an order of magnitude as well as in training time using PhML-DyR.