Existing LLM-based medical question answering systems lack citation generation and evaluation capabilities, raising concerns about their adoption in practice. In this work, we introduce MedCite, the first end-to-end framework that facilitates the design and evaluation of LLM citations for medical tasks. Meanwhile, we introduce a novel multi-pass retrieval-citation method that generates high-quality citations.Our extensive evaluation highlights the challenges and opportunities of citation generation for medical tasks, while identifying important design choices that have a significant impact on the final citation quality. Our proposed method achieves superior citation precision and recall improvements compared to strong baseline methods, and we show that our evaluation results correlate well with annotation results from professional experts.