As post-transcriptional regulators of gene expression, micro-ribonucleic acids (miRNAs) are regarded as potential biomarkers for a variety of diseases. Hence, the prediction of miRNA-disease associations (MDAs) is of great significance for an in-depth understanding of disease pathogenesis and progression. Existing prediction models are mainly concentrated on incorporating different sources of biological information to perform the MDA prediction task while failing to consider the fully potential utility of MDA network information at the motif-level. To overcome this problem, we propose a novel motif-aware MDA prediction model, namely MotifMDA, by fusing a variety of high- and low-order structural information. In particular, we first design several motifs of interest considering their ability to characterize how miRNAs are associated with diseases through different network structural patterns. Then, MotifMDA adopts a two-layer hierarchical attention to identify novel MDAs. Specifically, the first attention layer learns high-order motif preferences based on their occurrences in the given MDA network, while the second one learns the final embeddings of miRNAs and diseases through coupling high- and low-order preferences. Experimental results on two benchmark datasets have demonstrated the superior performance of MotifMDA over several state-of-the-art prediction models. This strongly indicates that accurate MDA prediction can be achieved by relying solely on MDA network information. Furthermore, our case studies indicate that the incorporation of motif-level structure information allows MotifMDA to discover novel MDAs from different perspectives. The data and codes are available at https://github.com/stevejobws/MotifMDA.