This work proposes a novel privacy-preserving cyberattack detection framework for blockchain-based Internet-of-Things (IoT) systems. In our approach, artificial intelligence (AI)-driven detection modules are strategically deployed at blockchain nodes to identify real-time attacks, ensuring high accuracy and minimal delay. To achieve this efficiency, the model training is conducted by a cloud service provider (CSP). Accordingly, blockchain nodes send their data to the CSP for training, but to safeguard privacy, the data is encrypted using homomorphic encryption (HE) before transmission. This encryption method allows the CSP to perform computations directly on encrypted data without the need for decryption, preserving data privacy throughout the learning process. To handle the substantial volume of encrypted data, we introduce an innovative packing algorithm in a Single-Instruction-Multiple-Data (SIMD) manner, enabling efficient training on HE-encrypted data. Building on this, we develop a novel deep neural network training algorithm optimized for encrypted data. We further propose a privacy-preserving distributed learning approach based on the FedAvg algorithm, which parallelizes the training across multiple workers, significantly improving computation time. Upon completion, the CSP distributes the trained model to the blockchain nodes, enabling them to perform real-time, privacy-preserved detection. Our simulation results demonstrate that our proposed method can not only mitigate the training time but also achieve detection accuracy that is approximately identical to the approach without encryption, with a gap of around 0.01%. Additionally, our real implementations on various blockchain consensus algorithms and hardware configurations show that our proposed framework can also be effectively adapted to real-world systems.