Trustworthiness in healthcare question-answering (QA) systems is important for ensuring patient safety, clinical effectiveness, and user confidence. As large language models (LLMs) become increasingly integrated into medical settings, the reliability of their responses directly influences clinical decision-making and patient outcomes. However, achieving comprehensive trustworthiness in medical QA poses significant challenges due to the inherent complexity of healthcare data, the critical nature of clinical scenarios, and the multifaceted dimensions of trustworthy AI. In this survey, we systematically examine six key dimensions of trustworthiness in medical QA, i.e., Factuality, Robustness, Fairness, Safety, Explainability, and Calibration. We review how each dimension is evaluated in existing LLM‐based medical QA systems. We compile and compare major benchmarks designed to assess these dimensions and analyze evaluation‐guided techniques that drive model improvements, such as retrieval‐augmented grounding, adversarial fine‐tuning, and safety alignment. Finally, we identify open challenges—such as scalable expert evaluation, integrated multi‐dimensional metrics, and real‐world deployment studies—and propose future research directions to advance the safe, reliable, and transparent deployment of LLM‐powered medical QA.