Background: Maternal pregnancy-related anxiety (PRA) is reportedly related to neurodevelopmental outcomes of infants. However, the relationship between maternal PRA and the processing of emotions in the infant brain has not been extensively studied with neuroimaging. The objective of the present pilot study is to investigate the relationship between maternal PRA and infant hemodynamic responses to emotional speech at two months of age. Methods: The study sample included 19 mother-infant dyads from a general sample of a population of Caucasian mothers. Self-reported Pregnancy-Related Anxiety Questionnaire (PRAQ-R2) data was collected from mothers during pregnancy at gestational weeks (gwks) 24 (N = 19) and 34 (N = 18). When their infants were two months old, the infants’ brains functional responses to emotional speech in the left fronto-temporoparietal cortex were recorded using diffuse optical tomography (DOT). Results: Maternal PRAQ-R2 scores at gwk 24 correlated negatively with the total hemoglobin (HbT) responses to sad speech on both sides of the temporoparietal junction (Spearman's rank correlation coefficient ρ = -0.87). The correlation was significantly greater at gwk 24 than gwk 34 (ρ = -0.42). Limitations: The field of view of the measurement did not include the right hemisphere or parts of the frontal cortex. The sample size is moderate and the mothers were relatively highly educated, thus there may be some differences between the study sample and the general population. Conclusions: Maternal pregnancy-related anxiety may affect child brain emotion processing development. Further research is needed to understand the functional and developmental significance of the findings.