Driver fatigue is an important factor in traffic accidents, and the development of a detection system for driver fatigue is of great significance. To estimate and prevent driver fatigue, various classifiers based on electroencephalogram (EEG) signals have been developed; however, as EEG signals have inherent non-stationary characteristics, their detection performance is often deteriorated by background noise. To investigate the effects of noise on detection performance, simulated Gaussian noise, spike noise, and electromyogram (EMG) noise were added into a raw EEG signal. Four types of entropies, including sample entropy (SE), fuzzy entropy (FE), approximate entropy (AE), and spectral entropy (PE), were deployed for feature sets. Three base classifiers (K-Nearest Neighbors (KNN), Support Vector Machine (SVM), and Decision Tree (DT)) and two ensemble methods (Bootstrap Aggregating (Bagging) and Boosting) were employed and compared. Results showed that: (1) the simulated Gaussian noise and EMG noise had an impact on accuracy, while simulated spike noise did not, which is of great significance for the future application of driver fatigue detection; (2) the influence on noise performance was different based on each classifier, for example, the robust effect of classifier DT was the best and classifier SVM was the weakest; (3) the influence on noise performance was also different with each feature set where the robustness of feature set FE and the combined feature set were the best; and (4) while the Bagging method could not significantly improve performance against noise addition, the Boosting method may significantly improve performance against superimposed Gaussian and EMG noise. The entropy feature extraction method could not only identify driver fatigue, but also effectively resist noise, which is of great significance in future applications of an EEG-based driver fatigue detection system.