Robust medical image classification under input corruption and bag-level annotation remains a critical challenge in clinical AI applications. We propose \textbf{QAPNet}, a Quantum-Attentive Patchwise Network that integrates quantum neural encoding, additive attention-based instance reweighting, and prototype-contrastive regularization for reliable diagnosis from degraded inputs. Our framework uses a sliding-window strategy to divide each MRI medical Image into overlapping patches where each encoded via an 8-qubit quantum circuit using $RY$-based noise-sensitive layers for yielding expressive low-dimensional representations without classical CNNs. A lightweight additive attention mechanism computes instance-wise importance weights that enable interpretable and noise-aware bag-level aggregation. To enhance robustness, we apply a contrastive loss that aligns clean and noisy embeddings and enforce prototype-guided clustering via class-wise centroids. We evaluate QAPNet across seven benchmark medical imaging datasets under three levels of additive Gaussian noise ($\sigma \in {5\%, 10\%, 30\%}$). QAPNet consistently outperforms eight strong baselines and achieves up to $+20.8\%$ higher accuracy in OASIS (with $30\%$ noise), $+17.7\%$ in PathMNIST and maintains stable performance ($<4\%$ degradation) in all settings. Ablation studies confirm the critical role of quantum encoding, attention-based aggregation, and prototype contrastive learning. These results suggest that QAPNet offers a scalable and interpretable architecture for noisy medical imaging tasks in the real world to bridge the quantum representation learning with robust clinical prediction.