Children are at risk of short- and long-term morbidity and mortality from COVID-19. We examine whether autistic children and children with mental health conditions have higher odds of underlying health conditions at high risk of severe disease from COVID-19. We use claims data from a national sample of Medicaid-enrolled children for the years 2008-2016. We examine: (1) children with claims for autism; and (2) a random sample of children covered by Medicaid, without autism claims but with mental health condition. The comparison group is a random sample of children without autism or any mental health condition. There were 888,487 autistic children, 423,397 with mental health conditions (but not autism or intellectual disability), and 932,625 children without autism or mental health condition. We found 29.5% of autistic children and 25.2% of children with mental health conditions had an underlying condition with high risk for severe illness from COVID, compared to 14.1% of children without these diagnoses. Autistic children had higher odds of having any underlying condition (odds ratio = 2.17; 99% confidence interval = 2.14-2.20), as did children with mental health conditions (odds ratio = 1.71; 99% confidence interval = 1.68-1.73), adjusting for basic demographic characteristics. Children with diagnoses of autism and mental health conditions may be at higher risk for severe COVID due to high-risk condition prevalence.