Background/Objectives: The COVID-19 pandemic reduced in-person pediatric visits in the United States by over 50%, while telehealth visits increased significantly. The national use of telehealth for children and the factors influencing their use have been rarely studied. This study aimed to investigate the prevalence of telehealth use during the COVID-19 pandemic and explore the potential factors linked to its use at the state level. Methods: A cross-sectional study of the National Survey of Children’s Health (2021–22) sponsored by the federal Maternal and Child Health Bureau was performed. We used the least absolute shrinkage and selection operator (LASSO) regression to predict telehealth use during the pandemic. A bar map showing the significant factors from the multivariable regression was created. Results: Of the 101,136 children, 15.25% reported using telehealth visits due to COVID-19, and 3.67% reported using telehealth visits due to other health reasons. The Northeast states showed the highest telehealth use due to COVID-19. In the Midwest and Southern states, children had a lower prevalence of telehealth visits due to other health reasons. The LASSO regressions demonstrated that telehealth visits were associated with age, insurance type, household income, usual source of pediatric preventive care, perceived child health, blood disorders, allergy, brain injury, seizure, ADHD, anxiety, depression, and special needs. Conclusions: This study demonstrated significant variability in the use of telehealth among states during the COVID-19 pandemic. Understanding who uses telehealth and why, as well as identifying access barriers, helps maximize telehealth potential and improve healthcare outcomes for all.