Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to collaborate distributedly without aggregating local data, thereby protecting patient privacy. However, the data heterogeneity caused by different MRI protocols, insufficient local training data, and limited communication bandwidth inevitably impair global model convergence and updating. In this paper, we propose a new algorithm, FedPR, to learn federated visual prompts in the null space of global prompt for MRI reconstruction. FedPR is a new federated paradigm that adopts a powerful pre-trained model while only learning and communicating the prompts with few learnable parameters, thereby significantly reducing communication costs and achieving competitive performance on limited local data. Moreover, to deal with catastrophic forgetting caused by data heterogeneity, FedPR also updates efficient federated visual prompts that project the local prompts into an approximate null space of the global prompt, thereby suppressing the interference of gradients on the server performance. Extensive experiments on federated MRI show that FedPR significantly outperforms state-of-the-art FL algorithms with < 6% of communication costs when given the limited amount of local data.