Maternal depression symptoms are common in pregnant women and can have negative effects on offspring’s emotional development. This study investigated the association between prenatal maternal depression symptoms (assessed with the Edinburgh Postnatal Depression Scale at 24 weeks of gestation) and auditory perception of emotional stimuli in 3-year-olds (n = 58) from the FinnBrain Birth Cohort Study. Using electroencephalography (EEG), we examined mismatch responses for happy, sad, and angry sounds presented among neutral stimuli. A positive association between maternal depression symptoms and the emotional mismatch responses in an early time window (80–120 ms) was found, indicating that brain responses of children of mothers with depressive symptoms were weaker to happy sounds, though the results did not survive Bonferroni correction. There were no clear associations in the sad and angry emotional categories. Our results tentatively support that the 3-year-old children of mothers with depression symptoms may be less sensitive to automatically detect happy sounds compared to children whose mothers do not display symptoms of depression.