The increasing number of medical devices in the Internet of Medical Things (IoMT) environment has raised significant cybersecurity concerns. These devices often have weak security features, poor design, and insufficient authentication protocols, making them vulnerable to cyberattacks and intrusions. To mitigate these threats, robust security measures are essential. This includes implementing strong security protocols, ensuring continuous security monitoring, enforcing regular updates, and maintaining a constant response plan. Additionally, designing an effective Intrusion Detection System (IDS) is crucial to safeguard patient data and devices. This paper systematically studies the current state of the literature and the essential methods for intrusion detection in the IoMT. Employing a selection process, the paper identifies 28 critical studies published between 2018 and April 2024. The intrusion detection mechanisms in the IoMT are divided into five categories: IDS based on artificial intelligence models, datasets used in IoMT for IDS, fundamental security requirements, intrusion detection processes, and evaluation metrics. This paper dissects the various mechanisms within each category in a meticulous and comprehensive analysis. Finally, the paper examines the challenges and open issues in developing IDSs in IoMT. By offering a roadmap for researchers to enhance IDSs in the IoMT, this paper has the potential to significantly impact the fields of computer engineering, cybersecurity, and healthcare, thereby contributing to the advancement of these crucial fields.