Medical knowledge bases (KBs) are known to be vital for tasks like clinical decision support and medical question answering, since they provide well-structured relational information between entities. One of the main challenges for querying a medical KB is the mismatch between the terms in the KB and the colloquial and imprecise terminology used in user queries. To address this challenge, we propose a domain-specific query relaxation approach that leverages rich medical domain vocabularies and their semantic relationships from external knowledge sources, such as taxonomies, ontologies, and semantic networks, to expand the vocabulary of KBs. Our main goal is to expand both the set of queries that we can answer, as well as the set of answers to the queries, over the medical KB. We introduce a lightweight adaptation method to customize and incorporate external knowledge sources to work with the existing KB, and propose a novel similarity metric to leverage the information content in the KB, the structural information in the external knowledge source, and the contextual information from user queries. We implement our proposed techniques for a medical KB, and use SNOMED CT as the external knowledge source. We experimentally demonstrate the effectiveness of our proposed method and the improved quality of query results in terms of both precision and recall, compared to state-of-the-art approaches. Finally, we conduct user studies to evaluate how much a conversational interface can benefit from our proposed method in terms of its query capability on the medical KB.