The majority of psychoacoustic research investigating sound localization has utilized stationary sources, yet most naturally occurring sounds are in motion, either because the sound source itself moves, or the listener does. In normal hearing (NH) listeners, previous research showed the extent to which sound duration and velocity impact the ability of listeners to detect sound movement. By contrast, little is known about how listeners with hearing impairments perceive moving sounds; the only study to date comparing the performance of NH and bilateral cochlear implant (BiCI) listeners has demonstrated significantly poorer performance on motion detection tasks in BiCI listeners. Cochlear implants, auditory protheses offered to profoundly deaf individuals for access to spoken language, retain the signal envelope (ENV), while discarding temporal fine structure (TFS) of the original acoustic input. As a result, BiCI users do not have access to low-frequency TFS cues, which have previously been shown to be crucial for sound localization in NH listeners. Instead, BiCI listeners seem to rely on ENV cues for sound localization, especially level cues. Given that NH and BiCI listeners differentially utilize ENV and TFS information, the present study aimed to investigate the usefulness of these cues for auditory motion perception. We created acoustic chimaera stimuli, which allowed us to test the relative contributions of ENV and TFS to auditory motion perception. Stimuli were either moving or stationary, presented to NH listeners in free field. The task was to track the perceived sound location. We found that removing low-frequency TFS reduces sensitivity to sound motion, and fluctuating speech envelopes strongly biased the judgment of sounds to be stationary. Our findings yield a possible explanation as to why BiCI users struggle to identify sound motion, and provide a first account of cues important to the functional aspect of auditory motion perception.