In the near future, COVID-19 vaccine efficacy trials in larger cohorts may offer the possibility to implement child and adolescent vaccination. The opening of the vaccination for these strata may play a key role in order to limit virus circulation, infection spreading towards the most vulnerable subjects, and plan safe school reopening. Vaccine hesitancy (VH) could limit the ability to reach the coverage threshold required to ensure herd immunity. The aim of this study was to investigate the prevalence and determinants of VH among parents/guardians toward a potentially available COVID-19 vaccination for children and adolescents. An online survey was performed in parents/guardians of children aged <18 years old, living in Bologna. Overall, 5054 questionnaires were collected. A vast majority (60.4%) of the parents/guardians were inclined to vaccinate, while 29.6% were still considering the opportunity, and 9.9% were hesitant. Highest vaccine hesitancy rates were detected in female parents/guardians of children aged 6–10 years, ≤29 years old, with low educational level, relying on information found in the web/social media, and disliking mandatory vaccination policies. Although preliminary, these data could help in designing target strategies to implement adherence to a vaccination campaign, with special regard to web-based information.