The integration of Artificial Intelligence (AI) into healthcare has the potential to revolutionize patient care, diagnostics, and treatment planning. However, this integration also introduces significant challenges related to data governance, privacy, and compliance with emerging regulations. The European Union’s (EU) AI Act proposes a comprehensive regulatory framework aimed at ensuring that AI systems are trustworthy and respect fundamental rights. This paper provides an in-depth analysis of the data governance requirements stipulated by the EU AI Act specifically within the context of healthcare AI. Furthermore, it explores strategies for compliance, examines the interplay with existing regulations such as the General Data Protection Regulation (GDPR), and addresses the ethical considerations inherent in deploying AI in healthcare settings.