Recently, significant progress has been made in text-based motion generation, enabling the generation of diverse and high-quality human motions that conform to textual descriptions. However, generating motions beyond the distribution of original datasets remains challenging, i.e., zero-shot generation. By adopting a divide-and-conquer strategy, we propose a new framework named Fine-Grained Human Motion Diffusion Model (FG-MDM) for zero-shot human motion generation. Specifically, we first parse previous vague textual annotations into fine-grained descriptions of different body parts by leveraging a large language model. We then use these fine-grained descriptions to guide a transformer-based diffusion model, which further adopts a design of part tokens. FG-MDM can generate human motions beyond the scope of original datasets owing to descriptions that are closer to motion essence. Our experimental results demonstrate the superiority of FG-MDM over previous methods in zero-shot settings. We will release our fine-grained textual annotations for HumanML3D and KIT on the project page https://sx0207.github.io/fg-mdm/