In the past decades, healthcare has witnessed a swift transformation from traditional specialist/hospital centric approach to a patient-centric approach especially in the smart healthcare system (SHS). This rapid transformation is fueled on account of the advancements in numerous technologies. Amongst these technologies, the Internet of medicals things (IoMT) play an imperative function in the development of SHS with regard to productivity of electronic devices in addition to reliability, accuracy. Recently, several researchers have shown interest to leverage the benefits of IoMT for the development of SHS by interconnecting with the existing healthcare services and available medical resources. Though the integration of IoMT within medical resources enable to revolutionize the patient healthcare service from reactive to proactive care system, the security of IoMT is still in its infancy. As IoMT are mainly employed to capture extremely sensitive individual health data, the security and privacy of IoMT is of paramount importance and very crucial in safeguarding the patient life which could otherwise adversely affect the patient health state and in worse case may also lead to loss of life. Motivated by this crucial requirement, several researchers in tandem to the advancement in IoMT technologies have continuously made noteworthy progress to tackle the security and privacy issues in IoMT. Yet, many possible potential directions exist for future investigation. This necessitates for a complete overview of existing security and privacy solutions in the field of IoMT. Therefore, this paper aims to canvass the literature on the most promising state-of-the-art solutions for securing IoMT in SHS especially in the light of security, privacy protection, authentication and authorization and the use of blockchain for secure data sharing. Finally, highlights the review outcome briefing not only the benefits and limitation of existing security and privacy solutions but also summarizing the opportunities and possible potential future directions that can drive the researchers of next decade to improve and shape their research committed on safe integration IoMT in SHS.