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Medical named entity recognition (NER) has wide applications in intelligent healthcare. Sufficient labeled data is critical for training accurate medical NER model. However, the labeled data in a single medical platform is usually limited. Although labeled datasets may exist in many different medical platforms, they cannot be directly shared since medical data is highly privacy-sensitive. In this paper, we propose a privacy-preserving medical NER method based on federated learning, which can leverage the labeled data in different platforms to boost the training of medical NER model and remove the need of exchanging raw data among different platforms. Since the labeled data in different platforms usually has some differences in entity type and annotation criteria, instead of constraining different platforms to share the same model, we decompose the medical NER model in each platform into a shared module and a private module. The private module is used to capture the characteristics of the local data in each platform, and is updated using local labeled data. The shared module is learned across different medical platform to capture the shared NER knowledge. Its local gradients from different platforms are aggregated to update the global shared module, which is further delivered to each platform to update their local shared modules. Experiments on three publicly available datasets validate the effectiveness of our method.