A Burnt-Out Case begins with an anonymous European (apparently wealthy, as he drinks whiskey and smokes cigars) riding "the Bishop's boat" on the Congo river into Africa. This man talks little, simply riding along as the boat makes customary stops at seminaries and docks along the way. Finally, it arrives at its final stop: a leproserie deep in the jungle.
This leproserie combines medical care -- overseen by Doctor Colin -- with a religious Order -- overseen by the Superior. Doctor Colin tells a leper, Deo Gratias, that he has been cured, but Deo Gratias has lost his identity in the course of the illness and does not wish to return to society. The Superior greets the Bishop's boat and meets the mysterious European, who introduces himself as Querry. He asks to stay at the leproserie and, though he is puzzled, the Superior agrees. On Doctor Colin's recommendation, he assigns Deo Gratias to work as Querry's servant.
Querry offers to be of what help he can to Doctor Colin, but refuses to tell Colin what he did for a living before arriving at the leproserie. Frustrated, Colin finally suggests that Querry make the long drive to Luc in order to pick up a piece of medical equipment. Querry agrees and leaves with Deo Gratias. In Luc, Querry finds the medical crate in the local cathedral. While picking up some food supplies for the Order, he is accosted by Rycker, a local palm-oil factory manager, who insists that he stay the night at his home.
Rycker reveals that he knows Querry's true identity -- he is an architect famous for designing churches and cathedrals. Rycker introduces Querry to his very young, childish wife, Marie, before engaging him in a tedious theological discussion. Rycker was formerly a seminary student and continues to think himself a deeply religious man.
Back at the leproserie, word of Querry's vocation spreads. Doctor Colin attempts to enlist Querry to help with the construction of a new hospital they'd planned and after a struggle Querry agrees.
One day, Deo Gratias -- whom Querry has grown used to -- wanders off into the woods. When he remains missing into the night, Querry goes off alone to find him. After walking for a long time, he finds Deo Gratias sunk into a marsh. Querry stays the night with him, consoling the young leper until dawn.
Rycker hears of this act and interprets it as the height of saintliness. He spreads the news of Querry's good Christian example far and wide, including at a dinner party that includes the governor of the territory. After the party, Rycker drunkenly forces sex on his poor wife. She closes her eyes and thinks of Querry.
Others begin to see Querry as a saint too, especially Father Thomas, an angst-ridden and enthusiastic priest at the leproserie. Thomas departs for a seminary and soon after, an obese English journalist named Parkinson arrives, intent on writing a story about Querry. Querry resists his attempt adamantly, declaring that he's not a Christian at all, but Parkinson ignores this confession and goes with the story that will sell -- Querry the modern-day saint.
After Parkinson's departure, Querry feels that the whole affair might blow over, allowing him to live the reclusive life he desires, but he has no such luck. Father Thomas returns from the seminary carrying a copy of Parkinson's story, which is even more maudlin than Querry feared. He learns that Rycker fed Parkinson most of his pious claptrap and determines to drive out to Rycker's house and put an end to it.
Querry meets Marie at Rycker's house, where her husband is ill with fever. He finds Marie quite upset and she reveals that she is likely pregnant. Querry offers to give her a lift into Luc to see a doctor and she asks him to clear this trip with her husband. During his interview with Rycker, however, Querry is too maddened by the Parkinson affair to remember Marie's entreaty. Marie comes with him to Luc anyway, leaving her husband to the care of his servant.
During their night in Luc, Querry tells Marie the story of his youth and disillusionment thinly disguised as a fairy tale. Delighted by their time together, Marie jokingly writes in her diary, "Spent night with Querry!" The next day, Marie learns that she is indeed pregnant -- distressing news, as Rycker does not want any children. Meanwhile, Querry and she meet Parkinson, who has returned to write more articles about Querry. On cue, Rycker also arrives, irate at Querry and Marie's escape together. He finds Marie's journal entry and accuses Querry of cuckolding him. Querry denies it, but Rycker remains unconvinced.
Querry returns to the leproserie just as the hospital is completed. During the ensuing party, the fathers receive a distressing phone call -- Marie Rycker has fled from her husband and is claiming to be pregnant with Querry's child. Querry finds this utterly ridiculous, and during an interview with Marie discovers that she invented the lie in order to escape Rycker, who was very angry after the scene in Luc. She says that because she thought about Querry on the night her baby was conceived, it is in fact somewhat his -- a logic that leaves Querry baffled.
Querry retreats to Doctor Colin's house, finding the doctor sympathetic. However, trouble's never far. Rycker and Parkinson take the ferry to the leproserie and Rycker seems intent on revenge. He finds Querry at Doctor Colin's house and, after Querry laughs (at himself, not Rycker), Rycker shoots the famous man dead.
The novel closes with the news that though Rycker is imprisoned, his crime is likely to be excused as "a crime of passion."