Observing clouds to understand the weather is a crucial method for people to forecast upcoming conditions. Utilizing content-based satellite cloud image retrieval allows for the swift discovery of comparable historical cloud images, significantly aiding meteorologists in their advanced investigations. Nevertheless, satellite cloud images often present complexities due to their inclusion of diverse cloud types, leading to inadequate retrieval outcomes when relying on conventionally employed single-label retrieval techniques. Despite notable accomplishments in cloud image retrieval applications utilizing deep neural networks, concerns regarding network interpretability undermine confidence in the model's deductive outcomes. This paper introduces the interpretable cloud image hash retrieval network (ICIHRN), a framework that employs a singular object-level global unit alongside multiple local feature units for the purpose of generating hash codes tailored to cloud image retrieval. Furthermore, an attention branching network is incorporated to enhance the model's focus on discriminative regions within the image. Additionally, a suppression module is implemented to progressively uncover complementary regions through the suppression of prominent areas in preceding layers and the amalgamation of relationships among activated regions. This ensures that each feature unit is endowed with distinctive semantic information, thereby imparting a level of interpretability to the retrieval outcomes. On this foundation, multi-label supervision is seamlessly integrated into the deep hash learning framework. This integration not only enhances the depiction of intricate semantic contents within cloud images but also boosts retrieval efficiency. Comprehensive experimental outcomes, grounded in the publicly accessible satellite cloud map dataset LSCIDMR-V2, demonstrate superior performance relative to other methods.