The rapid proliferation of Internet of Medical Things (IoMT) devices in healthcare has introduced significant cybersecurity challenges, including data breaches, Distributed Denial-of-Service (DDoS) attacks, and unauthorized access. Intrusion Detection Systems (IDS) leveraging machine learning (ML) and deep learning (DL) have emerged as critical solutions to safeguard sensitive patient data and ensure network integrity. The growing deployment of the Internet of Medical Things (IoMT) has revolutionized healthcare but simultaneously exposed it to evolving cybersecurity threats. This review paper explores the landscape of artificial intelligence (AI)-based intrusion detection systems (IDS) for securing smart healthcare infrastructures. It analyzes over 20 recent studies (2020–2024) covering diverse methodologies, including deep learning (DL), machine learning (ML), federated learning (FL), blockchain integration, and hybrid metaheuristic algorithms. By categorizing solutions based on architectural design, performance metrics, and real-time applicability, this review identifies critical trends, gaps, and future research directions. The findings highlight that while DL models such as LSTM, CNN, and hybrid frameworks achieve high detection rates, challenges remain in scalability, interpretability, and energy efficiency. The review concludes with recommendations for developing explainable, privacy-preserving, and low-latency IDS architectures tailored to healthcare IoT ecosystems.