Due to increasing reliance on cloud, distributed computing platforms, electronic health records (EHRs), Internet of Medical Things (IoMT), and other modern information systems, secure medical data governance has become increasingly difficult for healthcare companies. Dynamic trust evaluation, independent policy enforcement, and continuous monitoring of compliance in different healthcare ecosystems cannot be done through existing governance solutions. To manage data access, check trustworthiness of the system, enforce governance policies, detect anomalies, and assure compliance with regulations, a new Agentic AI-Based Medical Data Governance and Trust Management Framework that utilizes intelligent autonomous agents is introduced in the paper. To maintain patient confidentiality and increase efficiency, specialized intelligent agents collaborate through decision making, policy adaptation, and reasoning. Using a combination of explainable AI, blockchain-based audit trails, zero-trust security, and federated learning guarantees the reliability of data exchange in healthcare. The experiments have shown improvement in security robustness, policy compliance, trust score precision, and governance efficiency compared to existing governance frameworks. The presented solution provides intelligent, explainable, and scalable medical data governance framework for modern smart healthcare ecosystems.