Skin burns represent a major clinical concern due to their association with pain, functional impairment, sensory damage, and even life-threatening complications. Early and accurate assessment is critical for first aid, clinical intervention, and the prevention of secondary complications. However, conventional burn diagnosis remains highly dependent on visual inspection and clinical expertise, which can introduce subjectivity and delay timely decision-making. To address these limitations, a hybrid automated skin burn detection framework was proposed, integrating transformer-based feature extraction with classical machine learning classification. In this framework, discriminative visual features were extracted using multiple Vision Transformer (ViT) architectures, including ViT-B/16, ViT-L/16, ViT-B/32, and DINOv2 (a self-supervised Vision Transformer model). The extracted features were subsequently fused. Given the resulting high-dimensional feature space, dimensionality reduction was performed using the Chi-square (Chi$^2$) algorithm, through which 500 features were retained, reducing computational complexity and mitigating the risk of model overfitting. The reduced feature set was then employed for burn classification using six classifiers. Model effectiveness was assessed using accuracy, precision, sensitivity, and F1-score metrics. Experimental results demonstrated that the Support Vector Machine (SVM) classifier achieved the highest classification performance, yielding an accuracy of 82.29%. Comparable yet slightly lower accuracies were observed for the Light Gradient Boosting Machine (LGBM) (80.51%) and Extreme Gradient Boosting (XGBoost) (80.17%) classifiers. Overall, the proposed hybrid model consistently outperformed baseline models, highlighting its superior discriminative capability. These findings indicate that the proposed framework holds strong potential for integration into clinical decision support systems, offering a reliable and objective tool for automated skin burn detection.