Medical image segmentation plays a critical role in diagnosis and clinical decision-making. However, centralized model training on patient data raises significant privacy and ethical concerns. This paper proposes a hybrid federated edge intelligence framework that enables decentralized model training for medical image segmentation without compromising patient confidentiality. By combining edge computing and federated learning, the framework allows multiple healthcare institutions to collaboratively train models locally and share only the learned parameters with a global server. The approach is validated on the ISIC 2018 skin lesion dataset, demonstrating comparable segmentation accuracy to traditional centralized models while significantly reducing data transfer and preserving privacy. The study highlights the feasibility of privacy-preserving, real-time AI deployment in clinical environments, contributing toward a secure, scalable, and ethical digital healthcare ecosystem.