Vaccine willingness among the mass populace, as well as their proper knowledge and perception regarding vaccines and the vaccination process, may contribute extensively towards attaining their anticipated vaccination rates. The current study endeavored to ascertain the Bangladeshi population’s knowledge, perception, and willingness towards COVID-19 vaccination. Relevant information was collected from 1201 adults aged 18 years or older by employing an online-based survey from 1 to 30 July 2021. Descriptive statistics, the chi-square (χ2) test, and a binary logistic regression analysis were applied in order to compare the extent of knowledge and perception prevalent among different demographic groups and correlate such prevalence with respective vaccine willingness. The participants expressed mean (± standard deviation) knowledge and perception scores of 6.48 ± 1.13 out of 8 and 5.37 ± 1.22 out of 7, respectively. A multivariate analysis confirmed the significant association (p < 0.05) of gender, age, and family income with the knowledge score, whereas age and knowledge level significantly influenced perception. Current living area, family income, and age were considerable contributors to COVID-19 vaccine willingness. Overall vaccine willingness was found to be significantly curtailed by inadequate knowledge (AOR 0.514, CI 95% 0.401–0.658, p < 0.001) and perception (AOR 0.710, CI 95% 0.548–0.920, p = 0.010) among the participants. All of the concerned authorities’ efforts are warranted in order to improve public understanding, perception, and inclination towards vaccination.