The ongoing COVID-19 contagious disease caused by SARS-CoV-2 has disrupted global public health, businesses, and economies due to widespread infection, with 676.41 million confirmed cases and 6.77 million deaths in 231 countries as of February 07, 2023. To control the rapid spread of SARS-CoV-2, it is crucial to determine the potential determinants such as meteorological factors and their roles. This study examines how COVID-19 cases and deaths changed over time while assessing meteorological characteristics that could impact these disparities from the onset of the pandemic. We used data spanning two years across all eight administrative divisions, this is the first of its kind––showing a connection between meteorological conditions, vaccination, and COVID-19 incidences in Bangladesh. We further employed several techniques including Simple Exponential Smoothing (SES), Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Integrated Moving Average with explanatory variables (ARIMAX), and Automatic forecasting time-series model (Prophet). We further analyzed the effects of COVID-19 vaccination on daily cases and deaths. Data on COVID-19 cases collected include eight administrative divisions of Bangladesh spanning March 8, 2020, to January 31, 2023, from available online servers. The meteorological data include rainfall (mm), relative humidity (%), average temperature (°C), surface pressure (kPa), dew point (°C), and maximum wind speed (m/s). The observed wind speed and surface pressure show a significant negative impact on COVID-19 cases (−0.89, 95% confidence interval (CI): 1.62 to −0.21) and (−1.31, 95%CI: 2.32 to −0.29), respectively. Similarly, the observed wind speed and surface pressure show a significant negative impact on COVID-19 deaths (−0.87, 95% CI: 1.54 to −0.21) and (−3.11, 95%CI: 4.44 to −1.25), respectively. The impact of meteorological factors is almost similar when vaccination information is included in the model. However, the impact of vaccination in both cases and deaths model is significantly negative (for cases: 1.19, 95%CI: 2.35 to −0.38 and for deaths: 1.55, 95%CI: 2.88 to −0.43). Accordingly, vaccination effectively reduces the number of new COVID-19 cases and fatalities in Bangladesh. Thus, these results could assist future researchers and policymakers in the assessment of pandemics, by making thorough efforts that account for COVID-19 vaccinations and meteorological conditions.