There is limited information on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection clustering within families with children. We aimed to study the transmission dynamics of SARS-CoV-2 within families with children in Greece. We studied 23 family clusters of coronavirus disease 2019 (COVID-19). Infection was diagnosed by reverse-transcriptase polymerase chain reaction in respiratory specimens. The level of viral load was categorized as high, moderate, or low based on the cycle threshold values. There were 109 household members (66 adults and 43 children). The median attack rate per cluster was 60% (range: 33.4%-100%). An adult member with COVID-19 was the first case in 21 (91.3%) clusters. Transmission of infection occurred from an adult to a child in 19 clusters and/or from an adult to another adult in 12 clusters. There was no evidence of child-to-adult or child-to-child transmission. In total 68 household members (62.4%) tested positive. Children were more likely to have an asymptomatic SARS-CoV-2 infection compared to adults (40% vs 10.5%; P = .021). In contrast, adults were more likely to develop a severe clinical course compared with children (8.8% vs 0%; P = .021). In addition, infected children were significantly more likely to have a low viral load while adults were more likely to have a moderate viral load (40.7% and 18.6% vs 13.8% and 51.7%, respectively; P = .016). In conclusion, while children become infected by SARS-CoV-2, they do not appear to transmit infection to others. Furthermore, children more frequently have an asymptomatic or mild course compared to adults. Further studies are needed to elucidate the role of viral load on these findings.