Memory functions involve three stages: encoding, consolidation, and retrieval. Modulating effects of glucocorticoids (GCs) have been consistently observed for declarative memory with GCs enhancing encoding and impairing retrieval, but surprisingly, little is known on how GCs affect memory consolidation. Studies in rats suggest a beneficial effect of GCs that were administered during postlearning wake periods, whereas in humans, cortisol impaired memory consolidation when administered during postlearning sleep. These inconsistent results raise the question whether effects of GCs critically depend on the brain state during consolidation (sleep vs. wake). Here, we compare for the first time directly the effects of cortisol on memory consolidation during postlearning sleep and wakefulness in different measures of declarative memory. Cortisol (13 mg vs. placebo) was intravenously infused during a postlearning nap or a time-matched period of wakefulness after participants had encoded neutral and emotional text material. Memory for the texts was tested (a) by asking for the contents of the texts (“item” memory) and (b) for the temporal order of the contents within the texts (“relational” memory). Neither postlearning infusion of cortisol during sleep nor during wakefulness affected retention of content words of emotional or neutral texts. Critically, however, the retention of temporal order within the texts, known to rely most specifically on the hippocampus proper within the medial-temporal lobe memory system, was distinctly improved by cortisol infusion during the wake phase but impaired by cortisol during sleep. These results point toward fundamentally different mechanisms of hippocampal memory consolidation, depending on the brain state.