Perceiving faces and understanding emotions are key components of human social cognition. Prior research with adults and infants suggests that these social cognitive functions are supported by superior temporal cortex (STC) and medial prefrontal cortex (MPFC). We used functional near-infrared spectroscopy (fNIRS) to characterize functional responses in these cortical regions to faces in early childhood. Three-year-old children (n = 88, M(SD) = 3.15(.16) years) passively viewed faces that varied in emotional content and valence (happy, angry, fearful, neutral) and, for fearful and angry faces, intensity (100%, 40%), while undergoing fNIRS. Bilateral STC and MPFC showed greater oxygenated hemoglobin concentration values to all faces relative to objects. MPFC additionally responded preferentially to happy faces relative to neutral faces. We did not detect preferential responses to angry or fearful faces, or overall differences in response magnitude by emotional valence (100% happy vs. fearful and angry) or intensity (100% vs. 40% fearful and angry). In exploratory analyses, preferential responses to faces in MPFC were not robustly correlated with performance on tasks of early social cognition. These results link and extend adult and infant research on functional responses to faces in STC and MPFC and contribute to the characterization of the neural correlates of early social cognition.