The vast majority of studies that process and analyze neural signals are conducted on cloud computing resources, which is often necessary for the demanding requirements of Deep Neural Network (DNN) workloads. However, applications such as epileptic seizure detection stand to benefit from edge devices that can securely analyze sensitive medical data in real-time and personalised manner. In this work, we propose a novel neuromorphic computing approach to seizure detection using a surrogate gradient-based deep Spiking Neural Network (SNN), which consists of a novel Spiking ConvLSTM unit (SPCLU). We have trained, validated, and rigorously tested the proposed SNN model across three publicly accessible datasets, including Boston Children’s Hospital–MIT (CHB-MIT) dataset from the U.S., and the Freiburg (FB) and EPILEPSIAE intracranial EEG (iEEG) datasets from Germany. The average leave-one-out cross-validation AUC score for FB, CHB-MIT, and EPILEPSIAE datasets can reach 92.7%, 89.0%, and 81.1%, respectively, while the computational overhead and energy consumption are significantly reduced when compared to alternative state-of-the-art models, showing the potential for building an accurate hardware-friendly, low-power neuromorphic system. This is the first feasibility study using a deep Spiking Neural Network for seizure detection on several reliable public datasets.