Using our voice represent an exquisitely intricate act, recruiting a host of cognitive and motor functions. As such, the voice is bound to reflect many aspects of the internal state of the speaker: personality, infections, stress, emotions. Here, we investigate whether sleep deprivation in otherwise normal and healthy persons can be detected through machine-learning analysis of vocal recordings. In contrast to previous approaches, we use fully generic acoustic features, derived from auditory-inspired models of sound processing, together with recently-developed machine learning interpretation techniques. Our results show that sleep deprivation can be accurately detected from generic acoustic features of vocal recordings. Two main different types of features were impacted by sleep deprivation: one related to speech rhythms, the other related to the timbre of the voice. We speculate that these features reflect two distinct physiological processes: the cognitive control of speech production and an inflammatory effect of the vocal apparatus. Crucially, the relative balance of these two effects varied widely for each individual, suggesting that the voice may be used as a "sleep stethoscope" to better understand the variety of idiosyncratic responses to sleep deprivation. Moreover, the method we outline is fully general and could be applied to the future investigation of any type of vocal biomarkers using machine-learning techniques.