The manual diagnosis of diabetic retinopathy (DR) is often invasive, time-consuming, expensive, and prone to human error. Additionally, it can be subjective, depending on the clinician’s professional experience. Recently, automated computer-aided diagnosis (CAD) systems have significantly reduced the time and effort required for diagnosis while achieving superior performance compared to traditional methods. Researchers have extensively explored deep learning (DL) and convolutional neural networks (CNNs) for diagnosing DR from fundus images, yielding promising results and offering a viable alternative to conventional diagnostic approaches. In this study, a hybrid model named EffNet-SVM is proposed for the classification of DR and no DR cases using retinal fundus images. The model is trained and tested using the Asia Pacific Tele-Ophthalmology Society (APTOS) dataset, which includes both DR and no DR images. The EffNet-SVM utilizes EfficientNetV2-Small for feature extraction from input fundus images, and the extracted features are then classified using a support vector machine (SVM) with a radial basis function (RBF) kernel. The EffNet-SVM model outperformed eight state-of-the-art DL models from the literature, achieving the highest accuracy of 97.26%. Performance metrics validate that the proposed hybrid model can be effectively integrated into CAD systems for the automated analysis of fundus images.