The advent of internet medicine provides patients with unprecedented convenience in searching and communicating with doctors relevant to their diseases and desired treatments online. However, the current doctor recommendation systems fail to fully ensure the professionalism and interpretability of the recommended results. In this work, we formulate doctor recommendation as a ranking task and develop a large language model (LLM)-based pointwise ranking framework. Our framework ranks doctors according to their relevance regarding specific diseases-treatment pairs in a zero-shot setting. The advantage of our framework lies in its ability to generate precise and explainable doctor ranking results. Additionally, we construct DrRank, a new expertise-driven doctor ranking dataset comprising over 38 disease-treatment pairs. Experiment results on the DrRank dataset demonstrate that our framework significantly outperforms the strongest cross-encoder baseline, achieving a notable gain of +5.45 in the NDCG@10 score while maintaining affordable latency consumption. Furthermore, we comprehensively present the fairness analysis results of our framework from three perspectives of different diseases, patient gender, and geographical regions. Meanwhile, the interpretability of our framework is rigorously verified by three human experts, providing further evidence of the reliability of our proposed framework for doctor recommendation.