Forward suppression at the level of the auditory cortex has been suggested to subserve auditory stream segregation. Recent results in non-streaming stimulation contexts have indicated that forward suppression can also be observed in the inferior colliculus; whether this holds for streaming-related contexts remains unclear. Here, we used cardiac-gated fMRI to examine forward suppression in the inferior colliculus (and the rest of the human auditory pathway) in response to canonical streaming stimuli (rapid tone sequences comprised of either one repetitive tone or two alternating tones). The first stimulus is typically perceived as a single stream, the second as two interleaved streams. In different experiments using either pure tones differing in frequency or bandpass-filtered noise differing in inter-aural time differences, we observed stronger auditory cortex activation in response to alternating vs. repetitive stimulation, consistent with the presence of forward suppression. In contrast, activity in the inferior colliculus and other subcortical nuclei did not significantly differ between alternating and monotonic stimuli. This finding could be explained by active amplification of forward suppression in auditory cortex, by a low rate (or absence) of cells showing forward suppression in inferior colliculus, or both.