Little is known about the role of noncoding regions in the etiology of autism spectrum disorder (ASD). We examined three classes of noncoding regions: Human Accelerated Regions (HARs), which show signatures of positive selection in humans; experimentally validated neural Vista Enhancers (VEs); and conserved regions predicted to act as neural enhancers (CNEs). Targeted and whole genome analysis of >16,600 samples and >4900 ASD probands revealed that likely recessive, rare, inherited variants in HARs, VEs, and CNEs substantially contribute to ASD risk in probands whose parents share ancestry, which enriches for recessive contributions, but modestly, if at all, in simplex family structures. We identified multiple patient variants in HARs near IL1RAPL1 and in a VE near SIM1 and showed that they change enhancer activity. Our results implicate both human-evolved and evolutionarily conserved noncoding regions in ASD risk and suggest potential mechanisms of how changes in regulatory regions can modulate social behavior.