An integrated approach was used to estimate the number of COVID-19 patients related to air quality and meteorological phenomena. Additionally, the air quality during pre-lockdown, lockdown, and post-lockdown stages of the COVID-19 pandemic was assessed to determine the effect of the infection containment measures taken in Bangladesh during the pandemic. The air quality was assessed based on measurements of nitrogen dioxide (NO), sulfur dioxide (SO), ozone (O), carbon monoxide (CO), black carbon, particulate matter (PM and PM), and aerosol optical depth. Time-averaged maps of these parameters have been generated from NASA's (National Aeronautics and Space Administration) website. Values of these parameters have also been collected from a continuous air monitoring station (CAMS) located in Bangladesh's north-western city Rajshahi. The comparison shows that lockdown during the pandemic has brought significant improvements in air quality. However, the improvement was not sustained, since rapid increases in the air pollutant concentrations were observed in the post-lockdown period. Furthermore, Pearson correlation coefficients between each air quality variable and the daily new COVID-19 case rates were calculated. Different meteorological variables during the same time periods were determined to observe the variation in Rajshahi city. Relationships of these variables with the case rates were also established. Additionally, statistical analyses of the obtained data have been conducted for the measured variables using the Kruskal-Wallis test to assess the differences in the observed data among the pre-lockdown, lockdown, and post-lockdown periods. Dunn's "Q" test was employed to test if the variables showed significance statistical difference during the Kruskal-Wallis test for pairwise comparisons. From the study, it has been observed that both meteorological variables and air quality parameters have significant relationship with daily new COVID-19 case rates. Both positive and negative associations of these parameters with the COVID-19 case rates have been observed. Very high air pollution has been observed in the post-lockdown period. Thus, it is recommended that appropriate authorities undertake corrective measures to protect the environment in cities with large populations. This study provides guidance for decision makers and health officials for future research and potentially reducing the spread of COVID-19.