The immunity conferred by SARS-CoV-2 vaccines and infections reduces the transmission of the virus. To answer how the effect of immunity is shared between a reduction of infectiousness and an increased protection against infection, we examined >50,000 positive cases and >110,000 contacts from Geneva, Switzerland (June 2020 to March 2022). We assessed the association between secondary attack rate (i.e. proportion of new cases among contacts) and immunity from natural infection and/or vaccination, stratifying per four SARS-CoV-2 variants and adjusting for index cases and contacts’ socio-demographic characteristics and the propensity of the contacts to be tested. Here we show that immunity protected contacts from infection, rather than reducing infectiousness of index cases. Natural infection conferred the strongest immunity. Hybrid immunity did not surpass recent infection. Although of smaller amplitude, the reduction in infectiousness due to vaccination was less affected by time and by the emergence of new SARS-CoV-2 variants than the susceptibility to infection. These findings support the role of vaccine in reducing infectiousness and underscore the complementary role of interventions reducing SARS-CoV-2 propagation, such as mask use or indoor ventilation.