The study explores Agentic AI in healthcare as a subdomain of artificial intelligence capable of autonomous operation, decision-making and goal-directed behavior with minimal human intervention. It analyzes its core components, including agent design, decision mechanisms, task allocation, agent coordination and classification frameworks, as well as the integration of 6G network technologies. The case study illustrates the use in remote robotic surgery with higher responsiveness, accuracy and reliability. Agentic AI architectures powered by 6G enable efficient autonomous decision-making and coordinated task execution in complex healthcare workflows. The SWOT analysis reveals a strong potential for scalability and efficiency, but also challenges in ethical management, system robustness and security. The findings highlight a promising paradigm for remote and critical care, with the need to address trust, compliance and transparency.