Medical image segmentation is crucial for clinical diagnosis. The Segmentation Anything Model (SAM) serves as a powerful foundation model for visual segmentation and can be adapted for medical image segmentation. However, medical imaging data typically contain privacy-sensitive information, making it challenging to train foundation models with centralized storage and sharing. To date, there are few foundation models tailored for medical image deployment within the federated learning framework, and the segmentation performance, as well as the efficiency of communication and training, remain unexplored. In response to these issues, we developed Federated Foundation models for Medical image Segmentation (FedFMS), which includes the Federated SAM (FedSAM) and a communication and training-efficient Federated SAM with Medical SAM Adapter (FedMSA). Comprehensive experiments on diverse datasets are conducted to investigate the performance disparities between centralized training and federated learning across various configurations of FedFMS. The experiments revealed that FedFMS could achieve performance comparable to models trained via centralized training methods while maintaining privacy. Furthermore, FedMSA demonstrated the potential to enhance communication and training efficiency. Our model implementation codes are available at https://github.com/LIU-YUXI/FedFMS.