Disease dynamics, human mobility, and public policies co-evolve during a pandemic such as COVID-19. Understanding dynamic human mobility changes and spatial interaction patterns are crucial for understanding and forecasting COVID-19 dynamics. We introduce a novel graph-based neural network (GNN) to incorporate global aggregated mobility flows for a better understanding of the impact of human mobility on COVID-19 dynamics as well as better forecasting of disease dynamics. We propose a recurrent message passing graph neural network that embeds spatio-temporal disease dynamics and human mobility dynamics for daily state-level new confirmed cases forecasting. This work represents one of the early papers on the use of GNNs to forecast COVID-19 incidence dynamics and our methods are competitive to existing methods. We show that the spatial and temporal dynamic mobility graph leveraged by the graph neural network enables better long-term forecasting performance compared to baselines.