Despite recent advancements in federated learning (FL) for medical image diagnosis, addressing data heterogeneity among clients remains a significant challenge for practical implementation. A primary hurdle in FL arises from the non-IID nature of data samples across clients, which typically results in a decline in the performance of the aggregated global model. In this study, we introduce FedMRL, a novel federated multi-agent deep reinforcement learning framework designed to address data heterogeneity. FedMRL incorporates a novel loss function to facilitate fairness among clients, preventing bias in the final global model. Additionally, it employs a multi-agent reinforcement learning (MARL) approach to calculate the proximal term $(\mu)$ for the personalized local objective function, ensuring convergence to the global optimum. Furthermore, FedMRL integrates an adaptive weight adjustment method using a Self-organizing map (SOM) on the server side to counteract distribution shifts among clients' local data distributions. We assess our approach using two publicly available real-world medical datasets, and the results demonstrate that FedMRL significantly outperforms state-of-the-art techniques, showing its efficacy in addressing data heterogeneity in federated learning. The code can be found here~{\url{https://github.com/Pranabiitp/FedMRL}}.
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