The extent of high-level perceptual processing during sleep remains controversial. In wakefulness, perception of periodicities supports the emergence of high-order representations such as the pulse-like meter perceived while listening to music. Electroencephalography (EEG) frequency-tagged responses elicited at envelope frequencies of musical rhythms have been shown to provide a neural representation of rhythm processing. Specifically, responses at frequencies corresponding to the perceived meter are enhanced over responses at meter-unrelated frequencies. This selective enhancement must rely on higher-level perceptual processes, as it occurs even in irregular (i.e., syncopated) rhythms where meter frequencies are not prominent input features, thus ruling out acoustic confounds. We recorded EEG while presenting a regular (unsyncopated) and an irregular (syncopated) rhythm across sleep stages and wakefulness. Our results show that frequency-tagged responses at meter-related frequencies of the rhythms were selectively enhanced during wakefulness but attenuated across sleep states. Most importantly, this selective attenuation occurred even in response to the irregular rhythm, where meter-related frequencies were not prominent in the stimulus, thus suggesting that neural processes selectively enhancing meter-related frequencies during wakefulness are weakened during rapid eye movement (REM) and further suppressed in non-rapid eye movement (NREM) sleep. These results indicate preserved processing of low-level acoustic properties but limited higher-order processing of auditory rhythms during sleep.