In web environments, user preferences are often refined progressively as users move from browsing broad categories to exploring specific items. However, existing generative recommenders overlook this natural refinement process. Generative recommendation formulates next-item prediction as autoregressive generation over tokenized user histories, where each item is represented as a sequence of discrete tokens. Prior models typically fuse heterogeneous attributes such as ID, category, title, and description into a single embedding before quantization, which flattens the inherent semantic hierarchy of items and fails to capture the gradual evolution of user intent during web interactions. To address this limitation, we propose CoFiRec, a novel generative recommendation framework that explicitly incorporates the Coarse-to-Fine nature of item semantics into the tokenization process. Instead of compressing all attributes into a single latent space, CoFiRec decomposes item information into multiple semantic levels, ranging from high-level categories to detailed descriptions and collaborative filtering signals. Based on this design, we introduce the CoFiRec Tokenizer, which tokenizes each level independently while preserving structural order. During autoregressive decoding, the language model is instructed to generate item tokens from coarse to fine, progressively modeling user intent from general interests to specific item-level interests. Experiments across multiple public benchmarks and backbones demonstrate that CoFiRec outperforms existing methods, offering a new perspective for generative recommendation. Theoretically, we prove that structured tokenization leads to lower dissimilarity between generated and ground truth items, supporting its effectiveness in generative recommendation. Our code is available at https://github.com/YennNing/CoFiRec.