Accurately predicting individual-level infection state is of great value since its essential role in reducing the damage of the epidemic. However, there exists an inescapable risk of privacy leakage in the fine-grained user mobility trajectories required by individual-level infection prediction. In this paper, we focus on developing a framework of privacy-preserving individual-level infection prediction based on federated learning (FL) and graph neural networks (GNN). We propose Falcon, a Federated grAph Learning method for privacy-preserving individual-level infeCtion predictiON. It utilizes a novel hypergraph structure with spatio-temporal hyperedges to describe the complex interactions between individuals and locations in the contagion process. By organically combining the FL framework with hypergraph neural networks, the information propagation process of the graph machine learning is able to be divided into two stages distributed on the server and the clients, respectively, so as to effectively protect user privacy while transmitting high-level information. Furthermore, it elaborately designs a differential privacy perturbation mechanism as well as a plausible pseudo location generation approach to preserve user privacy in the graph structure. Besides, it introduces a cooperative coupling mechanism between the individual-level prediction model and an additional region-level model to mitigate the detrimental impacts caused by the injected obfuscation mechanisms. Extensive experimental results show that our methodology outperforms state-of-the-art algorithms and is able to protect user privacy against actual privacy attacks. Our code and datasets are available at the link: https://github.com/wjfu99/FL-epidemic.