The integration of Artificial Intelligence (AI) in Platform-as-a-Service (PaaS) healthcare systems presents unprecedented challenges for regulatory compliance and governance frameworks. This paper provides a comprehensive analysis of existing regulatory gaps in AI-enabled healthcare platforms and proposes a novel governance framework addressing these challenges. Through systematic examination of current regulations, including HIPAA, GDPR, and emerging AI-specific guidelines, we identify critical gaps in technical oversight, operational management, and ethical considerations. Our proposed framework introduces a risk-based approach to governance, incorporating privacy-by-design principles and continuous compliance monitoring mechanisms. The effectiveness of the framework is assessed through a case study of a PaaS implementation in the healthcare sector at the national level, which demonstrates the challenges and improvements to consider for regulatory compliance and risk management. Our findings contribute to the evolving discourse on AI regulation in healthcare and provide practical guidelines for implementing robust governance structures in interoperable healthcare platforms.