The Internet of Medical Things (IoMT) has risen to prominence as a possible backbone in the health sector, with the ability to improve quality of life by broadening user experience while enabling crucial solutions such as near real-time remote diagnostics. However, privacy and security problems remain largely unresolved in the safety area. Various rule-based methods have been considered to recognize aberrant behaviors in IoMT and have demonstrated high accuracy of misbehavior detection appropriate for lightweight IoT devices. However, most of these solutions have privacy concerns, especially when giving context during misbehavior analysis. Moreover, falsified or modified context generates a high percentage of false positives and sometimes causes a by-pass in misbehavior detection. Relying on the recent powerful consolidation of blockchain and federated learning (FL), we propose an efficient privacy-preserving framework for secure misbehavior detection in lightweight IoMT devices, particularly in the artificial pancreas system (APS). The proposed approach employs privacy-preserving bidirectional long-short term memory (BiLSTM) and augments the security through integrating blockchain technology based on Ethereum smart contract environment. The effectiveness of the proposed model is bench-marked empirically in terms of sustainable privacy preservation, commensurate incentive scheme with an untraceability feature, exhaustiveness, and the compact results of a variant neural network approach. As a result, the proposed model has a 99.93% recall rate, showing that it can detect virtually all possible malicious events in the targeted use case. Furthermore, given an initial ether value of 100, the solution's average gas consumption and Ether spent are 84,456.5 and 0.03157625, respectively.