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, affecting widespread cortical regions. The possible impacts of these regional alterations in terms of structural network effects have not previously been characterized. Inter-regional morphological covariance analysis can capture network connectivity between different cortical areas at the macroscale level. Here, we used cortical thickness data from 1455 individuals with ASD and 1560 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 average asymmetry of networks involving the fusiform, rostral middle frontal, and medial orbitofrontal cortex, involving 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 executive functions, language-related and sensorimotor processes. These findings provide a network-level characterization of altered left-right brain asymmetry in ASD, based on a large combined sample. Altered asymmetrical brain development in ASD may be partly propagated among spatially distant regions through structural connectivity.