While the COVID-19 pandemic has significantly impacted mental health, limited information exists on the relationship between COVID-19 infection and mental health disorders in children and adolescents. This study explored the association between COVID-19 infection, infection severity, and the risk of depression and anxiety among school-aged youth. Data from the 2019–2021 Utah All Payers Claims Database (APCD) was used to identify children and adolescents (aged 6–15 years in 2019) covered by private insurance or Medicaid. Depression and anxiety diagnoses in 2021 were identified using diagnosis codes. Entropy balancing was applied to balance baseline differences between youth with and without a COVID-19 infection in 2020. Weighted logistic regression was conducted to identify factors associated with incidence of depression and anxiety. A total of 154,579 subjects were included, with an average age of 10.8 years (SD: 2.8); 48% were female. Youth with a COVID-19 infection had a 49% higher likelihood of having new depression or anxiety diagnoses in 2021 (OR = 1.49, p < 0.01). Compared to youth without COVID-19 infection, those with moderate symptoms had a 40% higher likelihood (OR = 1.40, p < 0.01), and those with severe symptoms had a 60% higher likelihood (OR = 1.60, p < 0.01) of developing depression or anxiety. This population-level study found that COVID-19 infection, especially severe cases, is associated with an increased risk of depression and anxiety in children and adolescents. These findings underscore the importance of targeted mental health interventions for youth impacted by the infection.