Sharks represent the earliest group of jawed vertebrates and as such, they may provide original insight for understanding the evolution of sleep in more derived animals. Unfortunately, beyond a single behavioural investigation, very little is known about sleep in these ancient predators. As such, recordings of physiological indicators of sleep in sharks have never been reported. Reduced energy expenditure arising from sustained restfulness and lowered metabolic rate during sleep have given rise to the hypothesis that sleep plays an important role for energy conservation. To determine whether this idea applies also to sharks, we compared metabolic rates of draughtsboard sharks (Cephaloscyllium isabellum) during periods ostensibly thought to be sleep, along with restful and actively swimming sharks across a 24-h period. We also investigated behaviours that often characterise sleep in other animals, including eye closure and postural recumbency, to establish relationships between physiology and behaviour. Overall, lower metabolic rate and a flat body posture reflect sleep in draughtsboard sharks, whereas eye closure is a poorer indication of sleep. Our results support the idea for the conservation of energy as a function of sleep in these basal vertebrates.