Deep hash networks are widely used in tasks such as large-scale image retrieval due to high search efficiency and low storage costs through binary hash codes. With the growing demand for deploying deep hash networks on resource-constrained devices, it is crucial to perform network compression on them, in which automatic pruning constitutes a priority option owing to efficacy maintenance. However, most existing pruning methods are designed primarily for image classification tasks, which makes them suffer from efficacy degradation when transplanted to image retrieval tasks. In this paper, we propose a novel Automatic Channel Pruning framework by Searching with Structure Embedding (ACP-SSE). To the best of our knowledge, this is the first study to explore pruning techniques for deep hash networks and the first automatic pruning method by searching based on network topology structure. Specifically, we first design a structure encoding model by Graph Convolutional Networks (GCNs) whose graph is constructed by hash network and nodes' features are initialized by pruning strategies. The model is trained by contrastive learning loss efficiently without accuracy supervision by fine-tuning pruned models. In addition, we introduce a dynamic pruning search space in consideration of the resource constraints. By converting the automatic channel pruning task into searching the pruned structure with effect similar to the unpruned structure, it enables the method to adapt to various network architectures. Finally, the optimal networks are selected from the candidate set according to their performance in specific downstream tasks. Extensive experiments demonstrate that ACP-SSE indeed works in the automatic channel pruning area, outperforming state-of-the-art baselines in hashing-based image retrieval, while maintaining competitive accuracy in image classification. Our code is available in the supplementary material.