This study investigated the infectivity of severe acute respiratory syndrome (SARS-CoV-2) in individuals who re-tested positive for SARS-CoV-2 RNA after recovering from their primary illness. We investigated 295 individuals with re-positive SARS-CoV-2 polymerase chain reaction (PCR) test results and 836 of their close contacts. We attempted virus isolation in individuals with re-positive SARS-CoV-2 PCR test results using cell culture and confirmed the presence of neutralizing antibodies using serological tests. Viral culture was negative in all 108 individuals with re-positive SARS-CoV-2 PCR test results in whom viral culture was performed. Three new cases of SARS-CoV-2 infection were identified among household contacts using PCR. Two of the three new cases had had contact with the index patient during their primary illness, and all three had antibody evidence of past infection. Thus, there was no laboratory evidence of viral shedding and no epidemiological evidence of transmission among individuals with re-positive SARS-CoV-2 PCR test results.