The genetic basis of autism spectrum disorder (ASD) is known to consist of contributions from de novo mutations in variant-intolerant genes. We hypothesize that rare inherited structural variants in cis-regulatory elements (CRE-SVs) of these genes also contribute to ASD. We investigated this by assessing the evidence for natural selection and transmission distortion of CRE-SVs in whole genomes of 9274 subjects from 2600 families affected by ASD. In a discovery cohort of 829 families, structural variants were depleted within promoters and untranslated regions, and paternally inherited CRE-SVs were preferentially transmitted to affected offspring and not to their unaffected siblings. The association of paternal CRE-SVs was replicated in an independent sample of 1771 families. Our results suggest that rare inherited noncoding variants predispose children to ASD, with differing contributions from each parent.