Hypnos is a first-person narrative, written from the perspective of an unnamed character living in Kent and later London, England. The narrator writes that he fears sleep, and is resolved to write his story down lest it drive him further mad, regardless of what people think after reading it. The narrator, a sculptor, recounts meeting a mysterious man in a railway station. The moment the man opened his "immense, sunken, and widely luminous eyes", the narrator knew that the stranger would become his friend--"the only friend of one who had never possessed a friend before." In the eyes of the stranger, he witnessed important knowledge of the mysteries he always sought to learn. From this point on, he would touch his friend and sculpt him daily. At night they would commence their adventures, exploring worlds beyond human comprehension. Over time, the narrator's companion begins to speak of using their ability to transcend into the unknown as a way to rule the universe (via a set of drugs). The narrator is frightened by the prospect and disavows such hubris to the reader.

Soon the narrator is off on a foray with his friend, travelling through a void that he explains is beyond human sensation. Passing through several barriers, eventually the narrator comes to one he cannot cross, though his friend does. Opening his "physical eyes", the narrator wakes up and awaits the return of his friend, who awakes severely shaken and reticent, warning only that they must avoid sleep at all cost. From then on, with the aid of drugs, the two avoid sleep, as each time they succumb, they both seem to rapidly age and are plagued by nightmares that the narrator refuses to explain. The story ends with the narrator explaining that one night, his friend fell into a "deep-breathing sleep" and was impossible to arouse. The narrator shrieks, faints, and awakes surrounded by police and neighbors, who inform him that his friend was not real. There is only a bust of his friend in his room, engraved with the Greek word: _____ (Hypnos).