Agentic artificial intelligence (AI) is an emerging development in the digital transformation of healthcare. Unlike conventional generative AI, agentic AI systems can perform autonomous, goal-directed actions and coordinate complex tasks. They promise to support or even collaborate with clinicians and patients in increasingly independent ways. While agentic AI raises familiar moral concerns regarding safety, accountability and bias, this article focuses on a less explored dimension: its capacity to transform the moral fabric of healthcare itself. Drawing on the framework of techno-moral change and the three domains of decision, relation and perception, we investigate how agentic AI might reshape the patient–physician relationship and reconfigure core concepts of medical morality. We argue that these shifts, while not fully predictable, demand ethical attention before widespread deployment. Ultimately, the paper calls for integrating ethical foresight into the design and use of agentic AI.