As the exploration and utilization of outer space persist, the proliferation of space targets has significantly increased, underscoring the growing importance of space situational awareness. However, space target images encounter numerous challenges, including overexposure, excessive shadowing, star noise, and motion blur, distinct from natural images. While existing models can address specific issues in space target recognition images, their ability for generalizing to unseen data remains relatively weak. Furthermore, the uniform background and minimal interclass differences in space target images impose significant constraints on recognition accuracy. To tackle these challenges, we propose a domain-aware generalized meta-learning for space target recognition. In the meta-training phase, we introduce a distillation module to generalize the prior knowledge of auxiliary domains. This module distills features and predictions from auxiliary domains, providing prior information to develop a model capable of generalization across diverse domains. In the meta-testing phase, the frozen generalized embedding function is connected with a feature bias module to mitigate domain bias issues. Building on the advanced awareness of the space target domain, which is marked by substantial intraclass variations and minimal interclass variations, we introduce a feature refinement module. This module resolves fine-grained issues by reconstructing features and augmenting the proto loss to narrow the intraclass data distance. In practice, our method is evaluated under out-of-distribution settings on the BUAA-SID-share1.0 dataset, achieving an impressive accuracy of 96.0%, surpassing existing space target recognition algorithms.