Are you feeling anxious? Did you sleep poorly last night? Sleep disruption is a recognized feature of all anxiety disorders. Here, we investigate the basic brain mechanisms underlying the anxiogenic impact of sleep loss. Additionally, we explore whether subtle, societally common reductions in sleep trigger elevated next-day anxiety. Finally, we examine what it is about sleep, physiologically, that provides such an overnight anxiety-reduction benefit. We demonstrate that the anxiogenic impact of sleep loss is linked to impaired medial prefrontal cortex activity and associated connectivity with extended limbic regions. In contrast, non-rapid eye movement (NREM) slow-wave oscillations offer an ameliorating, anxiolytic benefit on these brain networks following sleep. Of societal relevance, we establish that even modest night-to-night reductions in sleep across the population predict consequential day-to-day increases in anxiety. These findings help contribute to an emerging framework explaining the intimate link between sleep and anxiety and further highlight the prospect of non-rapid eye movement sleep as a therapeutic target for meaningfully reducing anxiety.