Dialogue System for Medical Diagnosis (DSMD) based on reinforcement learning (RL) can simulate patient-doctor interactions, playing a crucial role in clinical diagnosis. However, due to the complexity of disease etiology, DSMD faces the challenges of low efficiency in diagnostic evidence search. Moreover, solely RL-based DSMS, without the constraints of professional medical knowledge, often generates irrational, meaningless, or even erroneous symptom inquiries, leading to poor interpretability of diagnostic path and high misdiagnosis rates. To address these issues, we propose an Evidence-based dialogue system with highly Interpretable Reasoning path for Automatic Diagnosis (EIRAD) grounded in medical knowledge graph (MKG). Specifically, our automated diagnostic model captures key symptoms for suspected diseases by explicitly leveraging the topology of MKG, enhancing the interpretability and accuracy of diagnosis. To expedite the retrieval of factual evidence, we develop two mechanisms: 1) Mapping mechanism between the entity set of MKG and DSMD's diagnostic evidence and diseases. According to the patient's symptoms, EIRAD prunes irrelevant disease and symptom nodes from the MKG, which can truncate the invalid action of RL-based DSMD. 2) Reward Mechanism of integrating the effectiveness of symptom inquiry and the accuracy of disease diagnosis. The comprehensive reward system is suitable for intelligent consultation, which can effectively drive DSMD to accelerate evidence collection. Experimental results demonstrate that our model significantly outperforms competitive benchmark methods in symptom inquiry efficiency and diagnostic accuracy.