Personalized medication aims to tailor healthcare to individual patient characteristics. However, the heterogeneity of patient data across healthcare systems presents significant challenges to achieving accurate and effective personalized treatments. Ethical concerns further complicate the aggregation of large volumes of data from diverse institutions. Federated Learning (FL) offers a promising decentralized solution by enabling collaborative model training through the exchange of client models rather than raw data, thus preserving privacy. However, existing FL methods often suffer from retrogression during server aggregation, leading to a decline in model performance in real-world medical FL settings. To address data variability in distributed healthcare systems, we introduce Federated Meta-Learning for Personalized Medication (FedMetaMed), which combines federated learning and meta-learning to create models that adapt to diverse patient data across healthcare systems. The FedMetaMed framework aims to produce superior personalized models for individual clients by addressing these limitations. Specifically, we introduce Cumulative Fourier Aggregation (CFA) at the server to improve stability and effectiveness in global knowledge aggregation. CFA achieves this by gradually integrating client models from low to high frequencies. At the client level, we implement a Collaborative Transfer Optimization (CTO) strategy with a three-step process - Retrieve, Reciprocate, and Refine - to enhance the personalized local model through seamless global knowledge transfer. Experiments on real-world medical imaging datasets demonstrate that FedMetaMed outperforms state-of-the-art FL methods, showing superior generalization even on out-of-distribution cohorts.