Speech enhancement seeks to extract clean speech from noisy signals. Traditional deep learning methods face two challenges: efficiently using information in long speech sequences and high computational costs. To address these, we introduce the Spiking Structured State Space Model (Spiking-S4). This approach merges the energy efficiency of Spiking Neural Networks (SNN) with the long-range sequence modeling capabilities of Structured State Space Models (S4), offering a compelling solution. Evaluation on the DNS Challenge and VoiceBank+Demand Datasets confirms that Spiking-S4 rivals existing Artificial Neural Network (ANN) methods but with fewer computational resources, as evidenced by reduced parameters and Floating Point Operations (FLOPs).