Background: High rates of population immunity are needed to control the COVID-19 pandemic. This study aimed to assess parents’ intention to have their children, aged 5–11 years, vaccinated against COVID-19 and its influencing factors in Thailand. Methods: A cross-sectional online survey was conducted before the nationwide COVID-19 vaccine rollout for children aged 5–11 years in Thailand. A sample of 542 parents with children in this age group was recruited online. Results: In total, 58.8% of parents intended to vaccinate their child against COVID-19. Logistic regression analysis revealed that influencing factors include child age, parents’ education, interactive/critical vaccine literacy, attitudes that the COVID-19 vaccine is safe and effective for children, that the vaccine can reduce the severity of COVID-19 in children, that there were other ways to prevent children from contracting COVID-19 superior to vaccination, and that COVID-19 vaccination in children can be fatal. The main reasons for having an intention to vaccinate their children included to reduce the severity of symptoms if infected with COVID-19 and to protect them from contracting COVID-19 when they go to school. Conclusions: Our study provides evidence regarding factors influencing parents’ intention to vaccinate their children. The findings can be used to design future interventions to promote COVID-19 vaccine uptake in children.