Electronic Health Record (EHR) retrieval plays a pivotal role in various clinical tasks, but its development has been severely impeded by the lack of publicly available benchmarks. In this paper, we introduce a novel public EHR retrieval benchmark, CliniQ, to address this gap. We consider two retrieval settings: Single-Patient Retrieval and Multi-Patient Retrieval, reflecting various real-world scenarios. Single-Patient Retrieval focuses on finding relevant parts within a patient note, while Multi-Patient Retrieval involves retrieving EHRs from multiple patients. We build our benchmark upon 1,000 discharge summary notes along with the ICD codes and prescription labels from MIMIC-III, and collect 1,246 unique queries with 77,206 relevance judgments by further leveraging powerful LLMs as annotators. Additionally, we include a novel assessment of the semantic gap issue in EHR retrieval by categorizing matching types into string match and four types of semantic matches. On our proposed benchmark, we conduct a comprehensive evaluation of various retrieval methods, ranging from conventional exact match to popular dense retrievers. Our experiments find that BM25 sets a strong baseline and performs competitively to the dense retrievers, and general domain dense retrievers surprisingly outperform those designed for the medical domain. In-depth analyses on various matching types reveal the strengths and drawbacks of different methods, enlightening the potential for targeted improvement. We believe that our benchmark will stimulate the research communities to advance EHR retrieval systems.