A retrospective observational study was conducted among healthcare workers (HCWs) in a tertiary paediatric hospital. The study covered the period before and after implementation of the vaccination programme and evaluated the incidence of new SARS-CoV-2 infections in both periods. Risk factors of the new SARS-CoV-2 infection and COVID-19 vaccine effectiveness was also assessed in a real-world setting. The overall incidence of SARS-CoV-2 infections among HCWs in the study period was 19.4% with a high proportion of asymptomatic individuals (45.1%). The incidence before vaccination was 16.6% and nurses had a higher risk of infection, while physicians had a reduced risk (OR 1.80, 95% CI 1.29–2.52; and OR 0.45, 95% CI 0.30–0.68). Within two months of implementation, the programme achieved a high (88.9%) vaccination coverage in our cohort, although some disparities in vaccination rates were observed. In particular, older individuals, physicians, those working in clinical settings, and those previously uninfected were more likely to be vaccinated. The overall incidence of SARS-CoV-2 infection after vaccination deployment was 6.3% (40.0% in unvaccinated individuals and 3.2% in individuals vaccinated with at least one dose). The estimated vaccine efficacy was high (95.0%) in fully vaccinated HCWs and similar to those observed previously in clinical trials and real-world settings.