The amplitude modulation following response (AMFR) is the steady-state auditory response signaling phase-locking to slow variations in the amplitude (AM) of auditory stimuli that provide fundamental acoustic information. From a developmental perspective, the AMFR has been recorded in sleeping infants, compared to sleeping or awake adults. The lack of AMFR recordings in awake infants limits conclusions on the development of phase-locking to AM. Moreover, previous studies assessing phase-locking to AM using non-speech carriers have not included slow AM rates (<20 Hz), which are particularly important for speech processing. This study aimed at disentangling these issues by recording the AMFR with electroencephalography: in awake infants (3-and 10-month-olds) and awake young adults and for both slow and faster modulation rates (8 and 40 Hz). The AMFR was observable at 8 Hz at all ages (40%, 60%, and 33% of significant AMFR at 3 months, 10 months, and adults, respectively), but only adults showed reliable responses at 40 Hz (6% of significant AMFR at both 3 and 10 months, 100% in adults), thus, ruling out the possibility that sleep has a suppressing effect on the response. This pattern might be explained by developmental differences in the sources of neural processing of faster AM rates.