Aim: This study investigated the association between mothers' migration background and infant regulatory problems and analysed the mediating role of maternal mental health. We also explored whether the child's sex, parity and length of residence moderated the effect of a maternal migrant background. Methods: Child health surveillance data from the Danish home visiting programme were used. Community health nurses followed infants from birth to 12 months of age. The source population comprised 103 813 infants born between 1 January 2008 and 31 December 2018. The final sample comprised 62 964 infants, including 3.4% with a refugee background. A maternal migrant background was the primary exposure. The results are presented as risk ratios (RR) and 95% confidence intervals (CI). Results: A maternal refugee background increased the risk of regulatory problems in offspring (RR 1.34, 95% CI: 1.18–1.51). The effect was partially mediated by maternal postpartum mental health concerns. The association between maternal refugee background and infant regulatory problems was more pronounced in first-time mothers (RR 1.80, 95% CI: 1.51–2.15). Conclusion: The risk of infant regulatory problems was higher in the first-born children of refugee mothers. First-time refugee parents may need tailored support to identify mental health needs and infants with regulatory problems.