Evidence shows that immigrants are often in better health than the native born—the so-called ‘immigrant health paradox’—and this advantage may extend to their children’s health. A commonly cited but rarely tested explanation is the ‘selectivity hypothesis’, positing that immigrants are healthier due to selection at origin based on health or socio-economic status (SES). Using 2007–19 Spanish birth registries, we investigate immigrant–native gaps in health at birth and whether they are explained by immigrants’ educational selectivity. We find that babies born to immigrants are less likely to be low birthweight (LBW) but are disadvantaged in terms of macrosomia and gestational age. Selectivity is associated with reduced LBW even after accounting for parental SES, explaining the lower risk among children of Northern African and Latin American immigrants but not across other parental country-of-birth groups. Selectivity is not associated with other birth outcomes. We confirm the selectivity hypothesis but question its universality across groups and health outcomes.