Maternal anxiety during pregnancy has been consistently shown to negatively affect offspring neurodevelopmental outcomes. However, little is known about the impact of positive maternal traits/states during pregnancy on the offspring. The present study was aimed at investigating the effects of the mother’s mindfulness and anxiety during pregnancy on the infant’s neurocognitive functioning at 9 months of age. Mothers reported mindfulness using the Freiburg Mindfulness Inventory and anxiety using the Symptom Checklist (SCL-90) at ±20.7 weeks of gestation. Event-related brain potentials (ERPs) were measured from 79 infants in an auditory oddball paradigm designed to measure auditory attention—a key aspect of early neurocognitive functioning. For the ERP responses elicited by standard sounds, higher maternal mindfulness was associated with lower N250 amplitudes (P < 0.01, η2 = 0.097), whereas higher maternal anxiety was associated with higher N250 amplitudes (P < 0.05, η2 = 0.057). Maternal mindfulness was also positively associated with the P150 amplitudes (P < 0.01, η2 = 0.130). These results suggest that infants prenatally exposed to higher levels of maternal mindfulness devote fewer attentional resources to frequently occurring irrelevant sounds. The results show that positive traits and experiences of the mother during pregnancy may also affect the unborn child. Emphasizing the beneficial effects of a positive psychological state during pregnancy may promote healthy behavior in pregnant women.