Recent advances in Retrieval-Augmented Generation (RAG) have enabled large language models (LLMs) to ground outputs in clinical evidence. However, connecting LLMs with external databases introduces the risk of contextual leakage: a subtle privacy threat where unique combinations of medical details enable patient re-identification even without explicit identifiers. Current benchmarks in healthcare heavily focus on accuracy, ignoring such privacy issues, despite strict regulations like Health Insurance Portability and Accountability Act (HIPAA) and General Data Protection Regulation (GDPR). To fill this gap, we present MedPriv-Bench, the first benchmark specifically designed to jointly evaluate privacy preservation and clinical utility in medical open-ended question answering. Our framework utilizes a multi-agent, human-in-the-loop pipeline to synthesize sensitive medical contexts and clinically relevant queries that create realistic privacy pressure. We establish a standardized evaluation protocol leveraging a pre-trained RoBERTa-Natural Language Inference (NLI) model as an automated judge to quantify data leakage, achieving an average of 85.9% alignment with human experts. Through an extensive evaluation of 9 representative LLMs, we demonstrate a pervasive privacy-utility trade-off. Our findings underscore the necessity of domain-specific benchmarks to validate the safety and efficacy of medical AI systems in privacy-sensitive environments.