Concept bottleneck models (CBMs) are inherently interpretable and intervenable neural network models, which explain their final label prediction by the intermediate prediction of high-level semantic concepts. However, they require target task training to learn input-to-concept and concept-to-label mappings, incurring target dataset collections and training resources. In this paper, we present zero-shot concept bottleneck models (Z-CBMs), which predict concepts and labels in a fully zero-shot manner without training neural networks. Z-CBMs utilize a large-scale concept bank, which is composed of millions of vocabulary extracted from the web, to describe arbitrary input in various domains. For the input-to-concept mapping, we introduce concept retrieval, which dynamically finds input-related concepts by the cross-modal search on the concept bank. In the concept-to-label inference, we apply concept regression to select essential concepts from the retrieved concepts by sparse linear regression. Through extensive experiments, we confirm that our Z-CBMs provide interpretable and intervenable concepts without any additional training. Code will be available at https://github.com/yshinya6/zcbm.