The frequency-following response (FFR) is an auditory evoked potential (AEP) that follows the periodic characteristics of a sound. Despite being a widely studied biosignal in auditory neuroscience, the neural underpinnings of the FFR are still unclear. Traditionally, FFR was associated with subcortical activity, but recent evidence suggested cortical contributions which may be dependent on the stimulus frequency. We combined electroencephalography (EEG) with an inhibitory transcranial magnetic stimulation protocol, the continuous theta burst stimulation (cTBS), to disentangle the cortical contribution to the FFR elicited to stimuli of high and low frequency. We recorded FFR to the syllable /ba/ at two fundamental frequencies (Low: 113 Hz; High: 317 Hz) in healthy participants. FFR, cortical potentials, and auditory brainstem response (ABR) were recorded before and after real and sham cTBS in the right primary auditory cortex. Results showed that cTBS did not produce a significant change in the FFR recorded, in any of the frequencies. No effect was observed in the ABR and cortical potentials, despite the latter known contributions from the auditory cortex. Possible reasons behind the negative results include compensatory mechanisms from the non-targeted areas, intraindividual variability of the cTBS effectiveness, and the particular location of our target area, the primary auditory cortex.