SARS-CoV-2 infection in children is less severe than it is in adults. We perform a longitudinal analysis of the early innate responses in children and adults with mild infection within household clusters. Children display fewer symptoms than adults do, despite similar initial viral load, and mount a robust anti-viral immune signature typical of the SARS-CoV-2 infection and characterized by early interferon gene responses; increases in cytokines, such as CXCL10 and GM-CSF; and changes in blood cell numbers. When compared with adults, the antiviral response resolves faster (within a week of symptoms), monocytes and dendritic cells are more transiently activated, and genes associated with B cell activation appear earlier in children. Nonetheless, these differences do not have major effects on the quality of SARS-CoV-2-specific antibody responses. Our findings reveal that better early control of inflammation as observed in children may be key for rapidly controlling infection and limiting the disease course.