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Diabetic Retinopathy (DR) is a leading cause of preventable blindness worldwide, requiring early and accurate multi-class grading to prevent vision loss. Conventional screening faces challenges due to specialist shortages and manual evaluation variability, while classical deep learning models struggle with subtle non-linear inter-class variations and lack clinical transparency. To address this, we propose an interpretable hybrid Quantum Convolutional Neural Network (QCNN) framework. The pipeline uses a fine-tuned DenseNet121 backbone to extract 1024-dimensional spatial features, which are compressed via a multi-layer classical bottleneck to a 4-dimensional latent vector. These features are mapped into a 4-qubit Variational Quantum Circuit (VQC) using parallel RX angle embedding and processed through parameterized RY/RZ rotations and circular CNOT entanglement gates to enhance representation capacity. Evaluated on 1,506 retinal fundus images mapped across three severity classes (No/Mild, Moderate, and Severe DR), an independent 20% holdout test set (N=302) yielded a certified multi-class accuracy of 84.10%, an F1-score of 0.83, an AUC of 0.95 for severe cases, and a real-time inference latency of 0.085 seconds per image. To ensure clinical trust, SHapley Additive exPlanations (SHAP) was integrated to backmap quantum expectations into pixel-level heatmaps, accurately highlighting localized microaneurysms and exudates. This framework demonstrates the feasibility of transparent, quantum-enhanced AI for real-time medical decision support.