In recent years, COVID‐19 has become the hottest topic. Various issues, such as epidemic transmission routes and preventive measures, have “occupied” several online social media platforms. Many rumors about COVID‐19 have also arisen, causing public anxiety and seriously affecting normal social order. Identifying a rumor at its very inception is crucial to reducing the potential harm of its evolution to society as a whole. However, epidemic rumors provide limited signal features in the early stage. In order to identify rumors with data sparsity, we propose a few‐shot learning rumor detection model based on capsule networks (CNFRD), utilizing the metric learning framework and the capsule network to detect the rumors posted during unexpected epidemic events. Specifically, we constructively use the capsule network neural layer to summarize the historical rumor data and obtain the generalized class representation based on the historical rumor data samples. Besides, we calculate the distance between the epidemic rumor sample and the historical rumor class‐wise representation according to the metric module. Finally, epidemic rumors are discriminated against according to the nearest neighbor principle. The experimental results prove that the proposed method can achieve higher accuracy with fewer epidemic rumor samples. This approach provided 88.92% accuracy on the Chinese rumor dataset and 87.07% accuracy on the English rumor dataset, which improved by 7% to 23% over existing approaches. Therefore, the CNFRD model can identify epidemic rumors in COVID‐19 as early as possible and effectively improve the performance of rumor detection.