Small average differences in the left-right asymmetry of cerebral cortical thickness have been reported in individuals with autism spectrum disorder (ASD) compared to typically developing controls. Although these alterations affect multiple and widespread cortical regional asymmetries, the extent to which specific structural networks might be affected remains unknown. Inter-regional morphological covariance analysis can capture network connectivity relations between different cortical areas at the macroscale level. Here, we used cortical thickness data from 1,455 individuals with ASD and 1,560 controls, across 43 independent datasets of the ENIGMA consortium's ASD Working Group, to assess hemispheric asymmetries of intra-individual structural covariance networks, using graph theory-based topological metrics. Compared with typical features of small-world architecture in controls, the ASD sample showed significantly altered asymmetry of hemispheric networks involving the fusiform, rostral middle frontal, and medial orbitofrontal cortex, driven by shifts toward higher randomization of the corresponding right-hemispheric networks in ASD. A network involving the superior frontal cortex showed decreased right-hemisphere randomization. Based on comparisons with meta-analyzed functional neuroimaging data, the altered connectivity asymmetry particularly affected networks that subserve working memory, executive functions, language, reading, and sensorimotor processes. Taken together, these findings provide new insights into how altered brain left-right asymmetry in ASD affects specific structural and functional brain networks. Altered asymmetrical brain development in ASD may be partly propagated among spatially distant regions through structural connectivity.