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An intelligent transportation system (ITS) is one of the core elements of smart cities, enhancing public safety and relieving traffic congestion. Detection and classification of critical vehicles, such as police cars and ambulances, passing through roadways form crucial use cases for ITS. This paper proposes a solution for detecting and classifying safety-critical vehicles on urban roadways using deep learning models. At present, a large-scale dataset for critical vehicles is not publicly available. The appearance scarcity of emergency vehicles and different coloring standards in various countries are significant challenges. To cope with the mentioned drawbacks and to address the unique requirements of our smart city project, we first generate a large-scale critical vehicle dataset, combining images retrieved from various sources with the support of the YOLO vehicle detection model. The classes of the generated dataset are: fire truck, police car, ambulance, military police car, dang erous truck, and standard vehicle. Second, we compare the performance of the Vision in Transformer (ViT) network against the traditional convolutional neural networks (CNNs) for the task of critical vehicle classification. Experimental results on our dataset reveal that the ViT-based solution reaches an average accuracy and recall of 99.39% and 99.34%, respectively.