The rapid advancement of artificial intelligence (AI) in healthcare has revolutionized the industry, offering significant improvements in diagnostic accuracy, efficiency, and patient outcomes. However, the increasing adoption of AI systems also raises concerns about their environmental impact, particularly in the context of climate change. This review explores the intersection of climate change and AI in healthcare, examining the challenges posed by the energy consumption and carbon footprint of AI systems, as well as the potential solutions to mitigate their environmental impact. The review highlights the energy-intensive nature of AI model training and deployment, the contribution of data centers to greenhouse gas emissions, and the generation of electronic waste. To address these challenges, the development of energy-efficient AI models, the adoption of green computing practices, and the integration of renewable energy sources are discussed as potential solutions. The review also emphasizes the role of AI in optimizing healthcare workflows, reducing resource waste, and facilitating sustainable practices such as telemedicine. Furthermore, the importance of policy and governance frameworks, global initiatives, and collaborative efforts in promoting sustainable AI practices in healthcare is explored. The review concludes by outlining best practices for sustainable AI deployment, including eco-design, lifecycle assessment, responsible data management, and continuous monitoring and improvement. As the healthcare industry continues to embrace AI technologies, prioritizing sustainability and environmental responsibility is crucial to ensure that the benefits of AI are realized while actively contributing to the preservation of our planet.