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Medical diagnostic image analysis (e.g., CT scan or X-Ray) using machine learning is an efficient and accurate way to detect COVID-19 infections. However, sharing diagnostic images across medical institutions is usually not allowed due to the concern of patients' privacy. This causes the issue of insufficient datasets for training the image classification model. Federated learning is an emerging privacy-preserving machine learning paradigm that produces an unbiased global model based on the received updates of local models trained by clients without exchanging clients' local data. Nevertheless, the default setting of federated learning introduces huge communication cost of transferring model updates and can hardly ensure model performance when data heterogeneity of clients heavily exists. To improve communication efficiency and model performance, in this paper, we propose a novel dynamic fusion-based federated learning approach for medical diagnostic image analysis to detect COVID-19 infections. First, we design an architecture for dynamic fusion-based federated learning systems to analyse medical diagnostic images. Further, we present a dynamic fusion method to dynamically decide the participating clients according to their local model performance and schedule the model fusion-based on participating clients' training time. In addition, we summarise a category of medical diagnostic image datasets for COVID-19 detection, which can be used by the machine learning community for image analysis. The evaluation results show that the proposed approach is feasible and performs better than the default setting of federated learning in terms of model performance, communication efficiency and fault tolerance.