Artificial Intelligence (AI) is increasingly being hailed as the key to the future of healthcare supply chain management in countries such as India, where healthcare is a particularly complex setting for an integrated supply chain. This review presents the various Data-driven Artificial Intelligence (AI) technologies such as Machine Learning (ML), Natural Language Processing (NLP), Computer Vision, and Robotic Process Automation (RPA) that help in the automation of essential processes like demand forecasting, inventory management, and cold chain logistics in an efficient and timely manner. AI helps deliver vital supplies on time and minimizes any disruptions of services by utilizing predictive analytics and real-time monitoring. However, high implementation costs, data privacy concerns, the need for integration with legacy systems, and a need for more skilled professionals are barriers to the adoption of AI computing. To extract the maximal potential AI can offer healthcare logistics, the issues above need to be addressed. Upcoming research directions include further development in quantum computing, IoT integration, and collaborative AI platforms to fulfill resilience and sustainability objectives for supply chains. The results underscore the potential of AI to transform health supply chains and provide an opportunity to realize more scalable, responsive, and efficient health services.