Graph masked autoencoders (GMAE) have emerged as a significant advancement in self-supervised pre-training for graph-structured data. Previous GMAE models primarily utilize a straightforward random masking strategy for nodes or edges during training. However, this strategy fails to consider the varying significance of different nodes within the graph structure. In this paper, we investigate the potential of leveraging the graph's structural composition as a fundamental and unique prior in the masked pre-training process. To this end, we introduce a novel structure-guided masking strategy (i.e., StructMAE), designed to refine the existing GMAE models. StructMAE involves two steps: 1) Structure-based Scoring: Each node is evaluated and assigned a score reflecting its structural significance. Two distinct types of scoring manners are proposed: predefined and learnable scoring. 2) Structure-guided Masking: With the obtained assessment scores, we develop an easy-to-hard masking strategy that gradually increases the structural awareness of the self-supervised reconstruction task. Specifically, the strategy begins with random masking and progresses to masking structure-informative nodes based on the assessment scores. This design gradually and effectively guides the model in learning graph structural information. Furthermore, extensive experiments consistently demonstrate that our StructMAE method outperforms existing state-of-the-art GMAE models in both unsupervised and transfer learning tasks. Codes are available at https://github.com/LiuChuang0059/StructMAE.