In the rapidly evolving healthcare sector, project management faces challenges due to the complexity and dynamic nature of its environment. Traditional methodologies including PMI PMBoK, and PRINCE2, combined with Agile, provide structured and adaptable approaches; however, the potential of the integration of artificial intelligence (AI) techniques is still underexplored. This study investigates how AI-driven tools, such as machine learning (ML) and predictive analytics, embedded with project management methodologies can improve project efficiency, decision-making, and resource management in the healthcare sector. Through a comprehensive literature review, we identify key AI technologies that augment task automation, real-time insights, and predictive capabilities within healthcare project management. This study presents statistical evidence from the literature on the percentage distribution of project management methodologies with key aspects including adaptability to AI, compliance, flexibility, stakeholder engagement and risk management. We discuss how a hybrid approach that leverages the strengths of PRINCE2/PMI, Agile, and AI can accelerate timelines, improve adaptability, and enhance stakeholder satisfaction. Despite challenges such as data privacy and compliance, this study presents a mapping of AI technologies and project management methodologies along with a conceptual design towards building a strategic framework that aligns AI advancements with organizational goals, optimizing healthcare project outcomes.