The COVID-19 pandemic is a global traumatic experience for citizens, especially during sensitive time windows of heightened plasticity such as pregnancy and neonatal life. Pandemic-related stress experienced by mothers during pregnancy may act as an early risk factor for infants’ regulatory capacity development by altering maternal psychosocial well-being (e.g., increased anxiety, reduced social support) and caregiving environment (e.g., greater parenting stress, impaired mother–infant bonding). The aim of the present longitudinal study was to assess the consequences of pandemic-related prenatal stress on infants’ regulatory capacity. A sample of 163 mother–infant dyads was enrolled at eight maternity units in northern Italy. They provided complete data about prenatal stress, perceived social support, postnatal anxiety symptoms, parenting stress, mother–infant bonding, and infants’ regulatory capacity at 3 months of age. Women who experienced emotional stress and received partial social support during pregnancy reported higher anxious symptoms. Moreover, maternal postnatal anxiety was indirectly linked to the infants’ regulatory capacity at 3 months, mediated by parenting stress and mother–infant bonding. Dedicated preventive interventions should be delivered to mothers and should be focused on protecting the mother–infant dyad from the detrimental effects of pandemic-related stress during the COVID-19 healthcare emergency.