Background: The process of mass immunization against COVID-19 may be impacted by vaccine reluctance despite intense and ongoing efforts to boost vaccine coverage. The COVID-19 vaccine is a crucial component for controlling the pandemic. To the best of our knowledge, we did not come across any study presenting the post-vaccination side-effect profile among the Sudanese population. Developing strategies to improve the vaccine acceptability and uptake necessitate evidence-based reports about vaccine’s side effects and acceptance. In this regard, this study aimed at estimating the prevalence of COVID-19 vaccine side-effects among the general population in Sudan. Methodology: A cross-sectional web-based quantitative study was conducted among the general population aged ≥18 years and residing in the Khartoum state of Sudan. A 30-item survey tool recorded the demographics, chronic diseases, allergy to other vaccines and COVID-19 vaccine side-effects after the first, second and booster doses. The data on the onset and duration of side-effects after each dose were also recorded. The distribution of side-effect scores after each dose of COVID-19 vaccine was compared using appropriate statistical methods. Results: A total of 626 participants were approached for this study. There was a preponderance of females (57.7%), and 19% of respondents had chronic diseases. The vaccination rate against COVID-19 was 55.8% (n = 349/626). The prevalence of side-effects after the first, second and booster doses were 79.7, 48 and 69.4%, respectively. Pain at the injection site, headache, fatigue, exhaustion and fever were the common side-effects after the first and second doses, while pain at the injection site, fatigue, headache and muscle pain were frequently reported after the booster dose. Most of these side-effects appeared within 6 h and resolved within one or two days following the administration of the vaccine dose. The average side-effects scores were 4.1 ± 4.4 (n = 349), 2.2 ± 3.6 (n = 202) and 3.5 ± 4.1 (n = 36) after the first, second and booster doses, respectively. The female gender had significantly higher side-effects after primary and booster doses. The age group 18-24 years indicated higher side-effects after the first dose compared to participants with ages ranging from 31 to 40 years (p = 0.014). Patients with chronic disease indicated significantly higher (p = 0.043) side-effects compared to those without any comorbid illness. Conclusions: This study showed a high prevalence of transient COVID-19 vaccine-related side-effects after primary and booster doses. However, these side-effects waned within 48 h. Pain at the injection site was the most common local side-effect, while fatigue, fever, headache and muscle pain were frequently reported systemic side-effects. The frequency of side-effects was more profound among females, young adults and those with comorbid conditions. These findings indicate that COVID-19 vaccines are safe and have side-effects as reported in the clinical trials of the vaccines. These results aid in addressing the ongoing challenges of vaccine hesitancy in the Sudanese population that is nurtured by widespread concerns over the safety profile.