Medication recommendation is a crucial task for intelligent healthcare systems. Previous studies mainly recommend medications with electronic health records (EHRs). However, some details of interactions between doctors and patients may be ignored or omitted in EHRs, which are essential for automatic medication recommendation. Therefore, we make the first attempt to recommend medications with the conversations between doctors and patients. In this work, we construct DIALMED, the first high-quality dataset for medical dialogue-based medication recommendation task. It contains 11, 996 medical dialogues related to 16 common diseases from 3 departments and 70 corresponding common medications. Furthermore, we propose a Dialogue structure and Disease knowledge aware Network (DDN), where a QA Dialogue Graph mechanism is designed to model the dialogue structure and the knowledge graph is used to introduce external disease knowledge. The extensive experimental results demonstrate that the proposed method is a promising solution to recommend medications with medical dialogues. The dataset and code are available at https://github.com/f-window/DialMed.