Voices are the most relevant social sounds for humans and therefore have crucial adaptive value in development. Neuroimaging studies in adults have demonstrated the existence of regions in the superior temporal sulcus that respond preferentially to voices. Yet, whether voices represent a functionally specific category in the young infant's mind is largely unknown. We developed a highly sensitive paradigm relying on fast periodic auditory stimulation (FPAS) combined with scalp electroencephalography (EEG) to demonstrate that the infant brain implements a reliable preferential response to voices early in life. Twenty-three 4-month-old infants listened to sequences containing non-vocal sounds from different categories presented at 3.33 Hz, with highly heterogeneous vocal sounds appearing every third stimulus (1.11 Hz). We were able to isolate a voice-selective response over temporal regions, and individual voice-selective responses were found in most infants within only a few minutes of stimulation. This selective response was significantly reduced for the same frequency-scrambled sounds, indicating that voice selectivity is not simply driven by the envelope and the spectral content of the sounds. Such a robust selective response to voices as early as 4 months of age suggests that the infant brain is endowed with the ability to rapidly develop a functional selectivity to this socially relevant category of sounds.