Driver drowsiness is identified as a critical factor in road accidents, necessitating robust detection systems to enhance road safety. This study proposes a driver drowsiness detection system, DrowzEE-G-Mamba, that combines Electroencephalography (EEG) with State Space Models (SSMs). EEG data, known for its sensitivity to alertness, is used to model driver state transitions between alert and drowsy. Compared to traditional methods, DrowzEE-G-Mamba achieves significantly improved detection rates and reduced false positives. Notably, it achieves a peak accuracy of 83.24% on the SEED-VIG dataset, surpassing existing techniques. The system maintains high accuracy across varying complexities, making it suitable for real-time applications with limited resources. This robustness is attributed to the combination of channel-split, channel-concatenation, and channel-shuffle operations within the architecture, optimizing information flow from EEG data. Additionally, the integration of convolutional layers and SSMs facilitates comprehensive analysis, capturing both local features and long-range dependencies in the EEG signals. These findings suggest the potential of DrowzEE-G-Mamba for enhancing road safety through accurate drowsiness detection. It also paves the way for developing powerful SSM-based AI algorithms in Brain-Computer Interface applications.