Oil spills are harmful, with negative environmental, social, and economic consequences. Generally, a risk-based framework involves preventing, detecting, and mitigating these undesirable events. Regarding detection, rapid oil spill identification is essential for mitigation, which fosters the use of automated procedures. Usually, automated oil spill detection involves radar images, computer vision, and machine learning techniques for classification. In this work, we propose a novel feature extraction method based on the q-Exponential probability distribution, named q-EFE. Such a model is suitable to account for atypical extreme pixel values, as it can have the power-law behavior. The q-EFE is combined with machine learning (ML) models, comprising a computer vision methodology to automatically classify images as “with oil spill” or “without oil spill”. We used a public dataset with 1112 Synthetic Aperture Radar (SAR) images to validate our methodology. Considering the proposed q-Exponential-based feature extraction, the SVM and XGB models outperformed deep learning models, including a ResNet50 one, and LBP and GLCM techniques for the biggest dataset size. The obtained results suggest that the proposed q-EFE can extract complex features from SAR images. Combined with ML models, it can perform image classification with satisfactory balanced accuracy.