Hyperspectral Imaging (HSI) excels in material identification and capturing spectral details and is widely utilized in various fields, including remote sensing and environmental monitoring. However, in real-world applications, HSI is often affected by Stray Light Interference (SLI), which severely degrades both its spatial and spectral quality, thereby reducing overall image accuracy and usability. Existing hardware solutions are often expensive and add complexity to the system, and despite these efforts, they cannot fully eliminate SLI. Traditional algorithmic methods, on the other hand, struggle to capture the intricate spatial–spectral dependencies needed for effective restoration, particularly in complex noise scenarios. Deep learning methods present a promising alternative because of their flexibility in handling complex data and strong restoration capabilities. To tackle this challenge, we propose MambaHR, a novel State Space Model (SSM) for HSI restoration under SLI. MambaHR incorporates state space modules and channel attention mechanisms, effectively capturing and integrating global and local spatial–spectral dependencies while preserving critical spectral details. Additionally, we constructed a synthetic hyperspectral dataset with SLI by simulating light spots of varying intensities and shapes across spectral channels, thereby realistically replicating the interference observed in real-world conditions. Experimental results demonstrate that MambaHR significantly outperforms existing methods across multiple benchmark HSI datasets, exhibiting superior performance in preserving spectral accuracy and enhancing spatial resolution. This method holds great potential for improving HSI processing applications in fields such as remote sensing and environmental monitoring.