Introduction: Early diagnosis of autism spectrum disorder (ASD) based on resting-state functional magnetic resonance imaging (rs-fMRI) is crucial for effective intervention and rehabilitation. Using rs-fMRI, functional brain networks (FBNs) are constructed to represent interactions among brain regions of interest (ROIs), and existing graph neural network–based methods, particularly Graph Attention Networks (GATs), have shown promise for FBN-based ASD diagnosis. However, most current approaches primarily aggregate ROIs through low-order pairwise interactions, while higher-order neighbors are incorporated only implicitly through increased network depth. This strategy often leads to over-smoothing of node representations and limits the capture of informative higher-order brain interactions. Methods: To address these challenges, we propose the Hierarchical Neighbor Integration Graph Attention Network (HiNIGAT), a general graph learning framework that explicitly models multi-order interactions in FBNs. Specifically, HiNIGAT introduces a multi-order attention mechanism that constrains each attention head to specialize in a distinct neighborhood order, enabling the model to capture brain interactions from local connectivity to global network structure. Furthermore, a bidirectional gated fusion strategy is proposed to adaptively integrate complementary information across multi-order features, facilitating effective local–global representation collaboration. Results: Experiments on the ABIDE-I dataset demonstrate the effectiveness of HiNIGAT. Discussion: The results highlight the importance of explicit multi-order integration for ASD diagnosis.