Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) breakthrough infections in vaccinated individuals and reinfections in previously infected individuals have become increasingly common. Such infections highlight a broader need to understand the contribution of vaccination, including booster doses, and natural immunity to the infectiousness of individuals with SARS-CoV-2 infections, especially in high-risk populations with intense transmission, such as in prisons. Here we show that both vaccine-derived and naturally acquired immunity independently reduce the infectiousness of persons with Omicron variant SARS-CoV-2 infections in a prison setting. Analyzing SARS-CoV-2 surveillance data from December 2021 to May 2022 across 35 California state prisons with a predominately male population, we estimate that unvaccinated Omicron cases had a 36% (95% confidence interval (CI): 31-42%) risk of transmitting infection to close contacts, as compared to a 28% (25-31%) risk among vaccinated cases. In adjusted analyses, we estimated that any vaccination, prior infection alone and both vaccination and prior infection reduced an index case's risk of transmitting infection by 22% (6-36%), 23% (3-39%) and 40% (20-55%), respectively. Receipt of booster doses and more recent vaccination further reduced infectiousness among vaccinated cases. These findings suggest that, although vaccinated and/or previously infected individuals remain highly infectious upon SARS-CoV-2 infection in this prison setting, their infectiousness is reduced compared to individuals without any history of vaccination or infection. This study underscores benefit of vaccination to reduce, but not eliminate, transmission.