Recent advancements in multimodal out-of-context (OOC) misinformation detection have made remarkable progress in checking the consistencies between different modalities for supporting or refuting image-text pairs. However, existing OOC misinformation detection methods tend to emphasize the role of internal consistency, ignoring the significant of external consistency between image-text pairs and external evidence. In this paper, we propose HiEAG, a novel Hierarchical Evidence-Augmented Generation framework to refine external consistency checking through leveraging the extensive knowledge of multimodal large language models (MLLMs). Our approach decomposes external consistency checking into a comprehensive engine pipeline, which integrates reranking and rewriting, apart from retrieval. Evidence reranking module utilizes Automatic Evidence Selection Prompting (AESP) that acquires the relevant evidence item from the products of evidence retrieval. Subsequently, evidence rewriting module leverages Automatic Evidence Generation Prompting (AEGP) to improve task adaptation on MLLM-based OOC misinformation detectors. Furthermore, our approach enables explanation for judgment, and achieves impressive performance with instruction tuning. Experimental results on different benchmark datasets demonstrate that our proposed HiEAG surpasses previous state-of-the-art (SOTA) methods in the accuracy over all samples.