Vocalizations play an important role in the daily life of nonhuman primates and are likely precursors of human language. Recent functional imaging studies in the highly vocal common marmoset (Callithrix jacchus) have suggested that medial prefrontal cortex area 32 may be a part of a vocalization-processing network but the response properties of area 32 neurons to auditory stimuli remain unknown. Here, we performed electrophysiological recordings in area 32 with high-density Neuropixels probes and characterized neuronal responses to a variety of sounds including conspecific vocalizations. More than half of the neurons in area 32 responded to conspecific vocalizations and other complex auditory stimuli. These responses exhibited dynamics consisting of an initially non-selective reduction in neural activity, followed by an increase in activity that immediately conveyed sound selectivity. Our findings demonstrate that primate mPFC area 32 plays a critical role in processing species-specific and biologically relevant sounds.