This study investigated Coronavirus disease 2019 (COVID-19) vaccine acceptance, and compared the potential factors influencing vaccine acceptance and hesitancy between public university (PuU) and private university (PrU) students in Bangladesh. An anonymous, self-administered questionnaire was sent to 640 PuU and 660 PrU students in Google Form between 25th September and 22nd November 2021, which resulted in the participation of 1034 (461 PuU vs. 573 PrU) respondents (response rate: 72.03% vs. 86.81%). The pooled vaccine acceptance rates among PuU and PrU students were almost similar (88.1%, 95% confidence interval (CI) 85.1–91.1 vs. 87.6%, 95% CI 84.6–90.6). Employing binary logistic regression to assess the association between various potential factors and vaccine acceptance, the study revealed that out of 10 predictors, ‘safety’ and ‘efficacy’ had highly significant positive associations with vaccine acceptance in both cohorts (P = 0.000, P = 0.005). ‘Political roles’ was found to have varied effects– a significant (P = 0.02) negative and a significant positive (P = 0.002) association with vaccine acceptance in PuU and PrU students, respectively. Additionally, ‘communication’ (P = 0.003) and ‘trust’ (P = 0.01) were found to have significant positive associations in PrU students while ‘rumours’ (P = 0.03) had negative association in PuU students. The odds of accepting the COVID-19 vaccine were 1.5 vs. 0.9 in PuU and PrU students. Although chi-square analysis did not show any significant association between gender and vaccine acceptance, discrepancies were found in the factors that potentially affect vaccine uptake decision between PuU and PrU students. COVID-19 vaccine uptake may be improved if vaccine-related information becomes available and is communicated to large numbers of people effectively. The implementation of multidisciplinary interventional educational programmes may also be considered as a preferred approach to improve student's engagement in pandemic awareness and vaccine readiness.