Background Vaccination of masses against coronavirus disease 2019 (COVID-19) is critical to overcome the pandemic and restore normalcy. However, vaccine refusal and hesitancy prevail in many countries. COVID-19 has rapidly spread in Saudi Arabia since 2020. The acceptance rate of COVID-19 vaccines has been investigated in adults aged >18 years in Saudi Arabia. This study aimed to understand the acceptance and hesitancy of parents to vaccinate children aged <12 years against COVID-19 in Saudi Arabia and identify strategies that can encourage their engagement. Methods We used an online cross-sectional survey distributed to parents who lived in all regions of Saudi Arabia to investigate parents’ views on the acceptability of a future COVID-19 vaccine for their children aged <12 years. Five hundred parents living in Saudi Arabia completed the survey. Results The survey indicated that mothers were more enthusiastic about participating in the study than fathers. The participant aged 37.31 ± 8.52 years. A total of 38.6% of participants refused to vaccinate their children. Additionally, 56% were unsure if the vaccine would cause serious side effects in children. A total of 48.8% of parents believed that the Pfizer vaccine was suitable for children, while 64.5% failed to decide whether to administer vaccines to their children. Conclusion Vaccine hesitancy remains a major problem worldwide. A lack of scientific evidence on vaccine efficacy, low education level, and reduced level of health education and promotion are the most common factors in parents in Saudi Arabia. However, some participants agreed to receive vaccines only to protect their family members, and due to governmental rules and school mandates. Therefore, vaccine efficacy and safety in children must be clearly communicated to the public. This information would aid in reducing the hesitancy of parents to vaccinate their children against COVID-19.