Vector Database Management Systems~(VDBMSs) have become critical in LLM-integrated applications, powering tasks such as Retrieval-Augmented Generation~(RAG) and long-term memory. However, their inherent complexity—stemming from high-dimensional data structures, diverse indexing strategies, and heterogeneous implementations—makes them prone to reliability issues, particularly crash bugs caused by boundary condition failures such as invalid configurations and mismatched data dimensions. These bugs can result in severe consequences, including data loss, corrupted indexes, and cascading downstream failures. To address this gap, we propose VDBFuzz, the first fuzzing framework specifically designed to detect crash bugs in VDBMSs through systematic boundary value testing. VDBFuzz systematically leverages techniques to collect high-quality seeds, generate edge-case inputs, and explore complex API interactions. We evaluated VDBFuzz on 8 representative VDBMSs, including native systems (e.g., Weaviate, Milvus), libraries (e.g., Faiss, hnswlib), and extended systems (e.g., pgvector, sqlite-vec). VDBFuzz achieved up to 3x higher code coverage compared to state-of-the-art tools such as RESTler and Schemathesis, uncovering 19 previously unknown crash bugs, including 13 memory corruption and 6 runtime exceptions. These results highlight VDBFuzz’s effectiveness in improving the robustness and reliability of VDBMSs.