The study aimed to determine how frequently the adverse events of the COVISHIELD vaccine occur among the Bangladeshi population. This cross-sectional study was conducted at Sheikh Russel Gastroliver Institute and Hospital, Mohakhali, Dhaka, Bangladesh, in May 2021. The inclusion criteria were the adult populations who received the 2nd dose of the COVISHELD vaccine and had passed 28 days following the completion of the 2nd dose. Three hundred and five persons fulfilling the inclusion criteria were asked over the telephone—based on a predesigned questionnaire. The rates of adverse events were 54.1% and 41.3% after the 1st and 2nd dose of vaccine, respectively, and the difference was statistically significant (p < 0.001). Pain at the injection site was the most common adverse event (32.5% following the 1st dose and 27.9% following the 2nd dose). All of the symptoms were mild and lasted for about 2 days. Age and comorbidities were significantly associated with the adverse events (p < 0.001). Neither doses had any vaccine-related life-threatening adverse event nor had any symptoms related to vaccine-related blood clotting. Nineteen persons (6.2%) had been diagnosed with COVID-19 after the 1st dose of vaccination, and three (1%) persons had been diagnosed with COVID-19 after the 2nd dose of vaccination. As no significant life-threatening adverse event was observed, this study might help reduce the hesitancy for vaccination among the population and thus help reduce transmission of this highly contagious virus.