Grasp detection is a fundamental robotic task critical to the success of many industrial applications. However, current language-driven models for this task often struggle with cluttered images, lengthy textual descriptions, or slow inference speed. We introduce GraspMamba, a new language-driven grasp detection method that employs hierarchical feature fusion with Mamba vision to tackle these challenges. By leveraging rich visual features of the Mamba-based backbone alongside textual information, our approach effectively enhances the fusion of multimodal features. GraspMamba represents the first Mamba-based grasp detection model to extract vision and language features at multiple scales, delivering robust performance and rapid inference time. Intensive experiments show that GraspMamba outperforms recent methods by a clear margin. We validate our approach through real-world robotic experiments, highlighting its fast inference speed.