Reliable hand gesture recognition is important for intelligent human–machine interaction, assistive technologies, and rehabilitation systems, where accurate interpretation of muscle-activation patterns is required. This study proposes an integrated explainable machine–deep learning framework for recognizing eight hand movements from surface electromyography signals. Signals acquired from five healthy participants using three forearm sensors were processed using wavelet packet transform, producing 96 time- and frequency-domain features from second-level db6 decomposition. XGBoost combined with SHAP analysis was employed to rank feature importance and optimize the input representation. XGBoost-based feature optimization identified a compact subset of 20 SHAP-ranked features that achieved 98.18% cross-validation accuracy, while reducing the feature count by 58.3% compared with the 48-feature configuration that produced the highest accuracy. The selected features were subsequently classified using a Mamba selective state-space model. Five-fold cross-validation produced a mean accuracy of 98.06 ± 0.18% and a mean Macro F1-score of 98.05%, while the held-out test set achieved 98.14% accuracy and 98.14% Macro F1-score. The results demonstrate that explainable feature selection combined with Mamba can provide accurate, compact, and interpretable hand gesture recognition for future human–machine interaction applications.