The Tiger's Wife depicts the relationship between Natalia, a young medical professional living in a country in the Balkans, and her grandfather, a celebrated doctor who has recently passed away. Obreht's novel begins with a memory of Natalia and her grandfather visiting the city zoo to see the tigers--a routine of theirs in Natalia's childhood. From there, the novel shifts closer to the present day: the adult Natalia and a friend of hers, Zora, are on their way to the town of Brejevina, where they will administer medicine to the orphans in a local monastery. During the trip, Natalia learns of her grandfather's death. Nonetheless, she continues on to the home of her hosts, Barba Ivan and his wife Nada.
New tasks and conflicts arise during Natalia's time in Brejevina. She encounters a group of relatives, who are trying to locate the remains of a long-buried cousin and whose children are unwell; she also travels to a small town, Zdrevkov, to retrieve her deceased grandfather's belongings. However, large portions of the narrative are structured as memories of Natalia's childhood and adolescence, which were shaped by the chaos and warfare that her generation as a whole encountered. She also relays a large amount of information about her grandfather and about two mysterious figures that shaped his life, the Deathless Man and the Tiger's Wife.
The Deathless Man, Gavran Gaile, met Natalia's grandfather on three separate occasions: in a town suffering from a public sickness, at a pilgrimage site, and in the town of Sarobor during a state of siege. During the first of these meetings, the Deathless Man makes a bet against Natalia's grandfather, who doubts that Gavran, or "Gavo,” is immortal: Natalia's grandfather pledges his prized copy of Kipling's The Jungle Book against Gavo, and loses the bet when Gavo survives a long time underwater. However, Gavo declines to take the pledged item. On the later occasions, the Deathless Man explains more about his background (he has been condemned to live eternally by his uncle) and reveals that his ideas about death and knowledge have evolved (he comes to believe that it is best never to tell people that they are going to die, so that they do not panic).
The Tiger's Wife, whose true name is never known, is a deaf-mute Muslim girl from the rural town of Galina, where Natalia's grandfather grew up. During World War II, a tiger escaped from the city zoo and made its way into the countryside, finally settling on Galina's outskirts. The Tiger's Wife, who had married the town butcher, fed the animal pieces of meat. Other villagers panicked, and some of the men--including the butcher, a stern and violent man named Luka--made a failed attempt to hunt the tiger down.
Over time, superstitions and fears spring up around the Tiger's Wife. Luka, who had once been a sensitive man and a musician of some skill, mysteriously disappears. The Tiger's Wife is then found to be pregnant: many villagers believe that she is carrying the devil's child, yet Natalia's grandfather and his grandmother, Mother Vera, show the isolated young woman some kindness. Determined to eradicate the tiger, the people of Galina enlist the help of Darisa the Bear, a celebrated hunter. Yet Darisa also fails. Evidence of his death is found by Marko Parovic (the same man who provides Natalia with much of her information about Galina and its lore). The men of the town are ready to take action against the Tiger's Wife. However, the town apothecary avoids a larger conflict by tricking the Tiger's Wife into drinking poison, and makes Natalia's grandfather an unknowing participant in this ruse.
By the end of the novel, the diggers have successfully unearthed their cousin. Natalia volunteers to stand watch in a vigil for them and, while doing so, discovers new information about her hosts: Barba Ivan has been pretending to be a spirit known as a mora (which collects grave offerings). He also tells Natalia about his deceased son, Arlo.
In her final section of reminiscences, Natalia states that she has kept Barba Ivan's activities a secret, and explains the fates of a few of her other companions. Zora now works at the Neurology Institute in Zurich, and Natalia's grandfather is regarded as a hero among younger doctors: after all, he had gone to Zdrevkov in an attempt to save two boys who had been injured by a land mine. Yet his copy of The Jungle Book has disappeared. For its part, the tiger continues to haunt the people of Galina, having achieved something like immortality in their minds, and in Natalia's.