Background: Vaccination is the most effective method to prevent the spread of infectious diseases and helps reduce mortality rate and economic costs associated with the pandemic. Despite these advantages, misinformation and rumors on vaccine safety and efficacy can lead to increased hesitation or fear towards vaccination. This study reports the incidence of adverse events following Covishield vaccination, their associated factors, medication used for their management, and attitudes about vaccine safety. Methods: A randomised cross-sectional study was conducted from the sample of Covishield-vaccinated individuals from a secondary hospital, two primary health centres, and 36 health posts in eastern Nepal. Individuals (n = 602) were randomly sampled from a population (N = 1013) who had received the first dose of Covishield, namely frontline workers and other high-risk populations. The second-round follow-up had 516 participants. Association of incidence and severity of post-vaccination events with socio-demographic variables, comorbidity status, and medication use were estimated. Results: Among the 79.9% of participants who reported adverse events after receiving the first dose, two-thirds of complaints were mild (67.4%, 95% CI 63.2–71.6) with the most common complaint being pain at the injection site (86.5%). Paracetamol or its combination were used in majority cases (95.2%). After the second dose, only 31.2% (95% CI 27.2–35.2) reported adverse events, the overwhelming majority of which were mild (95.7%) and required a lower frequency of medication (7.4% vs. 25.9%). Adverse Event following immunization were significantly associated with being 18–30 years old (χ2 = 16.9, df = 3, p < 0.001) and female gender (χ2 = 5.2, df = 1, p < 0.05). Prior to the first dose, 86.0% of participants (95% CI 83.3–88.8%) perceived the vaccine to be safe, and 96.0% recommended the vaccine post-vaccination, while 96.8% were interested in receiving the second dose.Conclusions: Overall, vaccination associated events were mild and majority were managed with paracetamol or its combination. Effective counselling about adverse events before vaccination should be prioritised to reduce hesitation and fear.