Clinical diagnosis is time-consuming, requiring intensive interactions between patients and medical professionals. While large language models (LLMs) could ease the pre-diagnostic workload, their limited domain knowledge hinders effective medical question generation. We introduce a Knowledge Graph-augmented LLM with active in-context learning to generate relevant and important follow-up questions, KG-Followup, serving as a critical module for the pre-diagnostic assessment. The structured medical domain knowledge graph serves as a seamless patch-up to provide professional domain expertise upon which the LLM can reason. Experiments demonstrate that KG-Followup outperforms state-of-the-art methods by 5% - 8% on relevant benchmarks in recall.