Sleep disturbances are associated with intrusive memories, but the neurocognitive mechanisms underpinning this relationship are poorly understood. Here, we show that an absence of sleep disrupts prefrontal inhibition of memory retrieval, and that the overnight restoration of this inhibitory mechanism is predicted by time spent in rapid eye movement (REM) sleep. The functional impairments arising from sleep loss are linked to a behavioural deficit in the ability to suppress unwanted memories, and coincide with a deterioration of deliberate patterns of self-generated thought. We conclude that sleep deprivation gives rise to intrusive memories via the disruption of neural circuits governing mnemonic inhibitory control, which may rely on REM sleep.