Medical image segmentation plays a crucial role in AI-assisted diagnostics, surgical planning, and treatment monitoring. Accurate and robust segmentation models are essential for enabling reliable, data-driven clinical decision making across diverse imaging modalities. Given the inherent variability in image characteristics across modalities, developing a unified model capable of generalizing effectively to multiple modalities would be highly beneficial. This model could streamline clinical workflows and reduce the need for modality-specific training. However, real-world deployment faces major challenges, including data scarcity, domain shift between modalities (e.g., CT vs. MRI), and privacy restrictions that prevent data sharing. To address these issues, we propose FedGIN, a Federated Learning (FL) framework that enables multimodal organ segmentation without sharing raw patient data. Our method integrates a lightweight Global Intensity Non-linear (GIN) augmentation module that harmonizes modality-specific intensity distributions during local training. We evaluated FedGIN using two types of datasets: an imputed dataset and a complete dataset. In the limited dataset scenario, the model was initially trained using only MRI data, and CT data was added to assess its performance improvements. In the complete dataset scenario, both MRI and CT data were fully utilized for training on all clients. In the limited-data scenario, FedGIN achieved a 12 to 18% improvement in 3D Dice scores on MRI test cases compared to FL without GIN and consistently outperformed local baselines. In the complete dataset scenario, FedGIN demonstrated near-centralized performance, with a 30% Dice score improvement over the MRI-only baseline and a 10% improvement over the CT-only baseline, highlighting its strong cross-modality generalization under privacy constraints.