The Delta variant of SARS-CoV-2 has caused many breakthrough infections in fully vaccinated individuals. While vaccine status did not generally impact the number of viral RNA genome copies in nasopharyngeal swabs of breakthrough patients, as measured by Ct values, it has been previously found to decrease the infectious viral load in symptomatic patients. We quantified the viral RNA, infectious virus, and anti-spike IgA in nasopharyngeal swabs collected from individuals asymptomatically infected with the Delta variant of SARS-CoV-2. Vaccination decreased the infectious viral load, but not the amount of viral RNA. Furthermore, vaccinees with asymptomatic infections had significantly higher levels of anti-spike IgA in their nasal secretions compared to unvaccinated individuals with asymptomatic infections. Thus, vaccination may decrease the transmission risk of Delta, and perhaps other variants, despite not affecting the amount of viral RNA measured in nasopharyngeal swabs.