Rhinoceros begins in a small town square where Jean, an efficient, refined young man, meets his semi-alcoholic and fully apathetic friend, Berenger, for a drink. Jean upbraids Berenger for his drinking habits and his aimlessness. Soon, a rhinoceros runs through the square (off-stage), shocking all the townspeople with the exception of the indifferent Berenger. Jean lectures Berenger about will-power while a rational Logician explains the concept of a syllogism to an old man. Berenger concedes that he has a crush on Daisy, a typist at his office, but worries that she favors Dudard, an up-and-coming co-worker. Jean recommends will-power and cultural self- improvement to garner Daisy's affections, and to improve his life in general. Another rhino rushes by and tramples a cat. The townspeople debate whether or not it was the same rhino and what breed it was. Berenger and Jean get in a fight over the physical specifics of the rhino, and Jean storms off after calling Berenger a drunkard. The townspeople ask the Logician to clear up confusion, but his lengthy analysis makes no progress. The townspeople vow to stop the rhinos. Berenger expresses remorse for fighting with Jean, then says he's too upset to culture himself as planned and instead drinks.

In Berenger's office, the co-workers argue with Botard, an old skeptic who doesn't believe in the rhinos. Berenger arrives late, but Daisy sneaks him in. The employees ask Berenger if he saw the rhino. Botard claims the illusory appearance of the rhino is an example of "collective psychosis." They return to work, proof-reading law proposals, and wonder where co-worker Mr. Boeuf is. Mrs. Boeuf rushes in and says her husband is sick and will be back in a few days. She tells them that she was just chased by a rhino, which is now downstairs. The rhino crushes the staircase it tries to ascend, stranding the workers. Mrs. Boeuf recognizes the rhino as her husband. Daisy telephones the fire station to rescue them. The men give Mrs. Boeuf practical advice for dealing with this setback, but she is too devoted to her rhino-husband and vows to stay with him. She jumps down to the ground floor and (off-stage) rides off on his back. More rhinos are reported in the town. The firemen arrive to help them out the window. Botard vows he'll solve the rhino-riddle. Berenger passes on an offer to drink with Dudard so he can visit Jean.

Jean coughs in bed at home. Berenger visits and apologizes for their argument the previous day. At first, Jean has no recollection at all about the rhinoceroses. Jean's voice grows more hoarse, a bump on his nose continues to grow, and his skin gets greener by the moment. He becomes more misanthropic and savage. Berenger informs him of Mr. Boeuf's transformation, which Jean applauds. He moves in and out of the bathroom, each time appearing and sounding more like a rhino. He pronounces humanism dead, sheds his itchy clothes, tries to run down Berenger, apologizes, and runs into the bathroom. Berenger is about to escape, but follows Jean into the bathroom to help him. Off-stage in the bathroom, Jean attacks Berenger. Berenger escapes and closes the bathroom door behind him (but is pierced by a rhino horn) as Jean, now a full-blown rhino, tries to break free. Berenger alerts the tenants in the building to the rhino's presence in the building, but everyone else has transformed as well. Berenger looks out the window, where a herd of rhinos march. The bathroom door is on the verge of breaking. Berenger throws himself against the wall and breaks through it. He runs through the street, yelling "Rhinoceros!"

Berenger wakes up from a nightmare in his room and inspects himself for any impending rhino-signs. Still human, he struggles not to drink, but eventually does. Dudard visits and they discuss Jean's transformation, which Berenger feels guilty about. They discuss the metamorphoses as an epidemic. Berenger takes another drink, under the premise that alcohol is an immunization. Dudard urges Berenger not to feel too guilty. Dudard reveals that Papillon, their boss, has turned into a rhinoceros. Berenger believes that for a man of Papillon's human stature to change, it must have been involuntary. Dudard considers the metamorphoses natural, while Berenger continues to find them abnormal. The flustered Berenger says he will seek the Logician's services in clearing this up. A herd of rhinos passes and Berenger spots the Logician's hat on a rhinoceros, a sign of metamorphosis, and vows not to become one as well.

Daisy visits Berenger, which makes Dudard jealous. Daisy appears not to care too deeply about the epidemic. She informs them that Botard has metamorphosed. Berenger can't believe it, but then later rationalizes it. Daisy and Dudard iterate that acclimating oneself to the rhinos is the best solution, but Berenger resists. They start to have lunch, but are interrupted by a crumbling wall outside. The fire station has been sacked, and the firemen have turned into rhinos. Dudard leaves; he wants to experience the epidemic first-hand. Berenger tries to stop him, but Daisy lets him go. Dudard soon turns into a rhino outside. The sights and sounds of the rhinos become more beautiful despite their savagery. Berenger laments Dudard's demise, and Daisy reminds Berenger that they have no right to interfere in other's lives. She pours some brandy for Berenger and removes his bandage—still no signs of a transformation. Berenger claims he will defend her. He blames himself and Daisy for contributing, through lack of sympathy, to the transformations of Jean and Papillon, respectively. Daisy convinces him to shrug off the guilt. The phone rings, but they hear only rhino trumpeting on the line. They turn to the radio for help, but the rhinos have taken that over, as well.

Upstairs, a rhino stampede disrupts the house's foundations. Daisy believes they must adapt to their new neighbors, but Berenger proposes they regenerate the human race, like Adam and Eve. Daisy finds the power of the rhinos seductive. Berenger slaps her, then apologizes and declares that he'll never surrender and that he will protect her. She pledges her loyalty to him. The noise of the rhinos becomes more musical to Daisy, though Berenger still finds it savage and argues with her. Daisy breaks up with him and leaves. Berenger barricades his room and plugs his ears. He doubts his own humanity. He inspects photographs and cannot recognize any of his former friends—but he does identify himself and hangs three of his pictures on the wall beside the rhino heads. They turn out to be pictures of unattractive people and, compared to the elegant rhino heads, are even more grotesque. He envies the bodies of the rhinos, but at the brink of desperation, he nevertheless decides that he will fight the rhinos.