Ambient Intelligence (AMI) represents a significant advancement in information technology that is perceptive, adaptable, and finely attuned to human needs. It holds immense promise across diverse domains, with particular relevance to healthcare. The integration of Artificial Intelligence (AI) with the Internet of Medical Things (IoMT) to create an AMI environment in medical contexts further enriches this concept within healthcare. This survey provides invaluable insights for both researchers and practitioners in the healthcare sector by reviewing the incorporation of AMI techniques in the IoMT. This analysis encompasses essential infrastructure, including smart environments and spectrum for both wearable and non-wearable medical devices to realize the AMI vision in healthcare settings. Furthermore, this survey provides a comprehensive overview of cutting-edge AI methodologies employed in crafting IoMT systems tailored for healthcare applications and sheds light on existing research issues, with the aim of guiding and inspiring further advancements in this dynamic field.