Driving safely is crucial to avoid death, injuries, or financial losses that can be sustained in an accident. Thus, a driver’s physical state should be monitored to prevent accidents, rather than vehicle-based or behavioral measurements, and provide reliable information in this regard. Electrocardiography (ECG), electroencephalography (EEG), electrooculography (EOG), and surface electromyography (sEMG) signals are used to monitor a driver’s physical state during a drive. The purpose of this study was to detect driver hypovigilance (drowsiness, fatigue, as well as visual and cognitive inattention) using signals collected from 10 drivers while they were driving. EOG signals from the driver were preprocessed to remove noise, and 17 features were extracted. ANOVA (analysis of variance) was used to select statistically significant features that were then loaded into a machine learning algorithm. We then reduced the features by using principal component analysis (PCA) and trained three classifiers: support vector machine (SVM), k-nearest neighbor (KNN), and ensemble. A maximum accuracy of 98.7% was obtained for the classification of normal and cognitive classes under the category of two-class detection. Upon considering hypovigilance states as five-class, a maximum accuracy of 90.9% was achieved. In this case, the number of detection classes increased, resulting in a reduction in the accuracy of detecting more driver states. However, with the possibility of incorrect identification and the presence of issues, the ensemble classifier’s performance produced an enhanced accuracy when compared to others.