Recent studies suggest shared genetic effects on both schizophrenia and brain structure, but it has been challenging to specify which genes mediate this pleiotropic association. We accessed genome-wide association data on schizophrenia (N=69,369 cases; 236,642 controls), and on three magnetic resonance imaging (MRI) metrics (surface area, cortical thickness, neurite density index) measured at 180 cortical areas (N=36,843). Using Hi-C-coupled MAGMA, we identified 61 genes that were significantly associated with both schizophrenia and one or more MRI metrics. Whole genome analysis demonstrated significant genetic covariation between schizophrenia and area or thickness of most cortical regions. Genetic similarity between cortical areas was strongly coupled to covariance of their MRI metrics, and genetic covariation between schizophrenia and cortical regional phenotypes was greatest in the hubs of the corresponding structural covariance network. Three genomic regions, on chromosomes 3p21, 17q21 and 11p11, were enriched for neurodevelopmental processes and consistently implicated in these pleiotropic associations between schizophrenia and cortical network organization.