Keyword spotting (KWS) is an essential task in speech processing. It is widely used in voice assistants and smart devices. Deep learning models like CNNs, RNNs, and Transformers have performed well in KWS. However, they often struggle to handle long-term patterns and stay efficient at the same time. In this work, we present Keyword Mamba, a new architecture for KWS. It uses a neural state space model (SSM) called Mamba. We apply Mamba along the time axis and also explore how it can replace the self-attention part in Transformer models. We test our model on the Google Speech Commands datasets. The results show that Keyword Mamba reaches strong accuracy with fewer parameters and lower computational cost. To our knowledge, this is the first time a state space model has been used for KWS. These results suggest that Mamba has strong potential in speech-related tasks.