Mental stress can lead to traffic accidents by reducing a driver’s concentration or increasing fatigue while driving. In recent years, demand for methods to detect drivers’ stress in advance to prevent dangerous situations increased. Thus, we propose a novel method for detecting driving stress using nonlinear representations of short-term (30 s or less) physiological signals for multimodal convolutional neural networks (CNNs). Specifically, from hand/foot galvanic skin response (HGSR, FGSR) and heart rate (HR) short-term input signals, first, we generate corresponding two-dimensional nonlinear representations called continuous recurrence plots (Cont-RPs). Second, from the Cont-RPs, we use multimodal CNNs to automatically extract FGSR, HGSR, and HR signal representative features that can effectively differentiate between stressed and relaxed states. Lastly, we concatenate the three extracted features into one integrated representation vector, which we feed to a fully connected layer to perform classification. For the evaluation, we use a public stress dataset collected from actual driving environments. Experimental results show that the proposed method demonstrates superior performance for 30-s signals, with an overall accuracy of 95.67%, an approximately 2.5–3% improvement compared with that of previous works. Additionally, for 10-s signals, the proposed method achieves 92.33% classification accuracy, which is similar to or better than the performance of other methods using long-term signals (over 100 s).