Children with chronic medical conditions are more susceptible to developing a serious negative outcome from corona virus disease 2019 (COVID-19) than healthy children. This study investigated the extent of COVID-19 vaccine hesitancy (VH) and its predictors in parents of children with chronic liver disease (CLD) in Egypt. Methods: A cross-sectional study was conducted at the National Liver Institute from September to October 2022, using a random sampling method. Data were collected using the validated Arabic version of parents’ attitudes about childhood vaccines (PACV) scale. Structural equation modeling (SEM) and discriminant analysis were used to identify direct and indirect determinants of VH. Results: Of the 173 participating parents, 81.5% hesitated to vaccinate their child. Relevant characteristics for hesitancy included being the mother of the child (88.2%), younger than 40 years (92.9%), illiterate (92%), unemployed (88.8%), without health insurance (87.8%), unvaccinated against COVID-19 (97.2%), refused to complete vaccinations (85.7%), and not having chronic disease (85.7%) (p < 0.05). Previous COVID-19 infection of children motivated vaccination (p < 0.0001). Median total PACV, attitude, and trust scores were significantly higher in the hesitant group than the vaccinated group (p = 0.023). SEM suggests that child age and family size have a direct effect, while education level, and income have indirect effects on parents’ hesitancy. The model showed acceptable goodness of fit (GFI = 0.994, CFI = 1, RMSEA < 0.0001). A 92.9% corrected classification of the discriminator VH variables was determined using the discriminant analysis model (safety and efficacy, attitude and trust, child age, and family size). Conclusions: Many socioeconomic factors significantly affect parents’ attitudes toward their child’s vaccination. Thus, increasing parents’ awareness of the importance of childhood vaccination, especially among this risky group, may enhance their decision-making ability regarding vaccinating their children.