Background To align with the 2030 vision of the World Health Organization (WHO) to ensure 90% of girls receive the HPV vaccine before turning 15, Bangladesh has recently started the (HPV) vaccine campaign nationwide. Therefore, our study aimed to assess the level of its acceptance among parents of eligible daughters in Bangladesh. Methods This nationwide cross-sectional study was conducted among the self-identified parents of daughters in the age group of 9–15 years between June 28 and August 2, 2023. A total of 2,151 parents were conveniently selected from all eight divisions of Bangladesh. Data was collected through face-to-face interviews using a semi-structured questionnaire. The Health Belief Model was used to appraise respondents’ beliefs concerning HPV and its vaccination. Adjusted odds ratios (AOR) with a corresponding 95% confidence interval (CI), and a p-value of <0.05 was considered statistically significant. R Studio (Version 2023.09.0+463) was used as an interface for data analysis, while R (the programming language) was used for statistical computations. Results The mean age of the study participants was 38.18 (±5.86) years. The overall acceptance rate of the HPV vaccine was 86.61% (95%CI: 85.09–88.02). The vaccine acceptance level was positively associated with all the domains of the HBM (p<0.001), except in the perceived barrier domain (p = 0.489). After adjustment for other factors, it was found that higher age was associated with a decreased acceptance (AOR: 0.92; 95% CI: 0.89–0.95). The urban residents exhibited 42% lower odds of vaccine acceptance than rural (AOR: 0.58; 95% CI: 0.36–0.92). Similarly, participants of the middle-income group had 44% lower odds than the lower-income group (AOR: 0.56; 95% CI: 0.32–0.97). Conclusion Our study found a reasonably good level of acceptance of the HPV vaccine among the parents of eligible daughters. Multiple factors such as younger age, urban residence, belonging to the middle income group, history of regular routine health check-ups, knowledge of cervical cancer, positive perception about benefits of the vaccine, and positive cues to actions were associated with HPV vaccine acceptance.