Numerous sensitive applications, such as healthcare and medical services, need reliable transmission as a prerequisite for the success of the new age of communications technology. Unfortunately, these systems are highly vulnerable to attacks like Sybil, where many false nodes are created and spread with deceitful intentions. Therefore, these false nodes must be instantly identified and isolated from the network due to security concerns and the sensitivity of data utilized in healthcare applications. Especially for life-threatening diseases like COVID-19, it is crucial to have devices connected to the Internet of Medical Things (IoMT) that can be believed to respond with high reliability and accuracy. Thus, trust-based security offers a safe environment for IoMT applications. This study proposes a blockchain-based fuzzy trust management framework (BFT-IoMT) to detect and isolate Sybil nodes in IoMT networks. The results demonstrate that the proposed BFT-IoMT framework is 25.43% and 12.64%, 12.54% and 6.65%, 37.85% and 19.08%, 17.40% and 8.72%, and 13.04% and 5.05% more efficient and effective in terms of energy consumption, attack detection, trust computation reliability, packet delivery ratio, and throughput, respectively, as compared to the other state-of-the-art frameworks available in the literature.