In Saudi Arabia, the Ministry of Health (MoH) has implemented strict rules to ensure COVID-19 vaccination uptake by the general public. However, there is hesitancy about COVID-19 vaccination among parents for their children worldwide. We aimed to determine the concerns, behaviors, perceptions, and hesitancy of COVID-19 vaccination among parents for their children in Saudi Arabia. Parents of children aged 5–11 years were included in this cross-sectional study. A total of 1507 responses were obtained using the convenience sampling technique. The data were analyzed using SPSS version 25.0 by applying descriptive and inferential statistics. Of the parents who responded, 74.5% believed that the COVID-19 vaccination could affect the genes of children, and 72.8% believed that the COVID-19 vaccination could have a greater number of positive impacts on the overall health of children. In total, 87% of the parents were satisfied with the vaccination services and effective policies of the MoH, Saudi Arabia. This study concluded that there is a greater need to increase public awareness regarding the beneficial impact of COVID-19 vaccination on the overall health of children. Effective awareness campaigns are also required to provide empirical information to the public that COVID-19 vaccination for children is safe and effective.