The rapid integration of Artificial Intelligence (AI) into medical diagnostics has raised pressing concerns about patient privacy, especially when sensitive imaging data must be transferred, stored, or processed. In this paper, we propose a novel framework for privacy-preserving diagnostic inference on encrypted medical images using a modified convolutional neural network (Masked-CNN) capable of operating on transformed or ciphered image formats. Our approach leverages AES-CBC encryption coupled with JPEG2000 compression to protect medical images while maintaining their suitability for AI inference. We evaluate the system using public DICOM datasets (NIH ChestX-ray14 and LIDC-IDRI), focusing on diagnostic accuracy, inference latency, storage efficiency, and privacy leakage resistance. Experimental results show that the encrypted inference model achieves performance comparable to its unencrypted counterpart, with only marginal trade-offs in accuracy and latency. The proposed framework bridges the gap between data privacy and clinical utility, offering a practical, scalable solution for secure AI-driven diagnostics.