Deep neural networks excel in radiological image classification but frequently suffer from poor interpretability, limiting clinical acceptance. We present MedicalPatchNet, an inherently self-explainable architecture for chest X-ray classification that transparently attributes decisions to distinct image regions. MedicalPatchNet splits images into non-overlapping patches, independently classifies each patch, and aggregates predictions, enabling intuitive visualization of each patch's diagnostic contribution without post-hoc techniques. Trained on the CheXpert dataset (223,414 images), MedicalPatchNet matches the classification performance (AUROC 0.907 vs. 0.908) of EfficientNetV2-S, while improving interpretability: MedicalPatchNet demonstrates improved interpretability with higher pathology localization accuracy (mean hit-rate 0.485 vs. 0.376 with Grad-CAM) on the CheXlocalize dataset. By providing explicit, reliable explanations accessible even to non-AI experts, MedicalPatchNet mitigates risks associated with shortcut learning, thus improving clinical trust. Our model is publicly available with reproducible training and inference scripts and contributes to safer, explainable AI-assisted diagnostics across medical imaging domains. We make the code publicly available: https://github.com/TruhnLab/MedicalPatchNet