The ethical integration of Artificial Intelligence (AI) in healthcare necessitates addressing fairness-a concept that is highly context-specific across medical fields. Extensive studies have been conducted to expand the technical components of AI fairness, while tremendous calls for AI fairness have been raised from healthcare. Despite this, a significant disconnect persists between technical advancements and their practical clinical applications, resulting in a lack of contextualized discussion of AI fairness in clinical settings. Through a detailed evidence gap analysis, our review systematically pinpoints several deficiencies concerning both healthcare data and the provided AI fairness solutions. We highlight the scarcity of research on AI fairness in many medical domains where AI technology is increasingly utilized. Additionally, our analysis highlights a substantial reliance on group fairness, aiming to ensure equality among demographic groups from a macro healthcare system perspective; in contrast, individual fairness, focusing on equity at a more granular level, is frequently overlooked. To bridge these gaps, our review advances actionable strategies for both the healthcare and AI research communities. Beyond applying existing AI fairness methods in healthcare, we further emphasize the importance of involving healthcare professionals to refine AI fairness concepts and methods to ensure contextually relevant and ethically sound AI applications in healthcare.