Background: Coronavirus disease 2019 (COVID-19) requires mass immunization to control the symptoms and global spread of severe acute respiratory syndrome coronavirus 2. Data from developed countries reported a high prevalence of parental COVID-19 vaccine hesitancy. However, parental vaccine hesitancy data in countries with low and middle income are scarce. The goal of this study was to assess the prevalence of parental vaccine hesitancy and identify subgroups with higher odds of vaccine hesitancy. Methods: A cross-sectional study was conducted on parents of children aged <18 years from October 10, 2021, to October 31, 2021. Parents aged ≥18 years underwent face-to-face interviews in randomly selected places in Bangladesh using a vaccine hesitancy questionnaire. Predictors were identified using binary logistic regression analysis. Results: Data from 2633 eligible parents were analyzed. Overall, 42.8% reported COVID-19 vaccine hesitancy for their youngest child. The final model suggested that children's age, parent's age, religion, occupation, monthly household income, permanent address, living location, the status of tobacco use, adherence with the regular government vaccination programs (other than COVID-19), perception about COVID-19 vaccine efficacy among Bangladeshi children, self-vaccination intention, report about family members' illness or death from COVID-19, and perceived COVID-19 threat were the independent predictors of parental vaccine hesitancy. Conclusions: Vaccine hesitation varied based on sociodemographic characteristics, religion, behavior, and perceived COVID-19 threat. Therefore, interventions focused on addressing vaccine hesitancy among subgroups are warranted.