<p>The Internet of Medical Things (IoMT) transforms healthcare by enabling remote monitoring, personalized treatments, and efficient data sharing while empowering patients. However, the rise of Quantum Computing (QC) poses significant security challenges to IoMT, as quantum principles such as superposition and entanglement threaten to break current cryptographic methods, exposing IoMT systems to unprecedented risks. Researchers are also developing post-quantum and quantum-resistant techniques to mitigate these threats. This paper comprehensively reviews recent advances in securing IoMT, focusing on post-quantum Blockchains, quantum Blockchains, and quantum machine learning. It offers an in-depth analysis of IoMT architecture, security needs, associated threats, and a detailed evaluation of Blockchain technologies and post-quantum cryptography. This study classifies emerging quantum-based security solutions, identifies key challenges, and suggests a taxonomy of IoMT security techniques. It discusses current challenges and future research directions for enhancing IoMT security in the quantum era, while also proposing a quantum IoMT framework. To the best of our knowledge, this is the first systematic review of its kind, making it a pioneering work in the field of IoMT security within a quantum context.</p>