In 1965, Rosemary Woodhouse (Mia Farrow), a bright but somewhat naive young housewife, and Guy (John Cassavetes), her husband, a struggling actor, moves into the Bramford, an opulent but antiquated New York City apartment building. The couple learns from the building's manager, Mr. Nicklas (Elisha Cook, Jr.), that their new residence was previously inhabited by Mrs. Gardenia, an elderly woman who had seemingly gone senile. Guy also discovers a dresser concealing a simple closet which contains nothing except a vacuum cleaner and a stack of folded towels. Their friend Hutch (Maurice Evans) tries to dissuade them from taking the apartment, informing them of some of the Bramford's rather unseemly history but, undeterred, Rosemary and Guy move into the building.
Rosemary meets a young woman, Terry Gionoffrio (Angela Dorian), a recovering drug addict whom an elderly, eccentric couple in the building, the Castevets, took in from the street. As Rosemary admires a pendant necklace the Castevets gave to Terry, she notices its strange smell. Returning home one night, Guy and Rosemary find that Terry has thrown herself to her death from the window of the Castevets' seventh-floor apartment.
Rosemary and Guy are quickly befriended by the Castevets, Minnie (Ruth Gordon) and Roman (Sidney Blackmer), whom they'd first met on the street the night of Terry's suicide. Minnie invites the Woodhouses to dinner and they reluctantly accept. Guy forms a bond with the Castevets. Minnie gives Terry's pendant to Rosemary, telling her it is a good luck charm and the odd smell is from a plant called "tannis root". Later, Guy lands a role in a play when the actor who was originally cast suddenly and inexplicably goes blind. Guy suggests that he and Rosemary have a baby.
On the night they plan to conceive, Minnie brings them individual cups of chocolate mousse. Rosemary finds hers has a chalky undertaste and surreptitiously throws it away after a few mouthfuls. Rosemary passes out and experiences what she perceives to be a strange dream in which she is raped by a demonic presence in front of Guy, the Castevets, and other Bramford tenants. When she wakes, she finds scratches on her body. Guy tells her that he had sex with her while she was unconscious because he did not want to pass up the moment for her to conceive.
Rosemary learns that she is pregnant and is due on June 28, 1966. She plans to receive obstetric care from Dr. Hill (Charles Grodin), who is recommended to her by her friend Elise (Emmaline Henry). However, the Castevets insist she see their good friend, Dr. Abraham Sapirstein (Ralph Bellamy), who says that Minnie will make Rosemary a daily drink which is more healthful than the usual vitamin pills.
For the first three months of her pregnancy, Rosemary suffers severe abdominal pains, loses weight, becomes unusually pale, and craves raw meat and chicken liver. Dr. Sapirstein insists the pain will subside soon, and assures her she has nothing to worry about. When Hutch sees Rosemary's gaunt appearance and hears that she is being fed the mysterious tannis root, he is disturbed enough to do some research. Before he can tell Rosemary his findings, he mysteriously falls into a coma. Rosemary holds a party for some friends, some of whom advise her to have herself checked by Dr. Hill, because the pain she is feeling could be a warning that something is wrong. Rosemary tells Guy her plan to see Dr. Hill, which angers Guy. However, the abdominal pain suddenly disappears. Rosemary's health and appearance also improves quickly, and she and Guy are finally happy once again.
Three months later, Hutch dies. He leaves Rosemary a book about witchcraft and it is delivered to her at his funeral along with the cryptic message: "The name is an anagram". Rosemary deduces that Roman Castevet is really Steven Marcato, the son of a former resident of the Bramford who was accused of being a Satanist. Rosemary suspects her neighbors and Dr. Sapirstein are part of a cult with sinister designs for her baby, and that Guy is cooperating with them in exchange for help in advancing his acting career.
Rosemary becomes increasingly disturbed and shares her fears and suspicions with Dr. Hill, who, assuming she is delusional, calls Dr. Sapirstein and Guy. They tell her that if she cooperates, neither she nor the baby will be harmed. The two men bring Rosemary home, where she briefly escapes them. Despite Rosemary locking them out, they enter the bedroom. Rosemary goes into labor and is sedated by Dr. Sapirstein. When she wakes, she is told the baby died.
In the hall closet, Rosemary discovers a secret door leading into the Castevet apartment and hears a baby's cries, revealing that her child is alive. She then finds a congregation made up of the building's tenants, as well as Dr. Sapirstein, gathered around her newborn son. When Rosemary pulls back the curtains of the crib, she is horrified and asks what they've done to its eyes. It is remarked upon that the baby, a boy, has "his father's eyes," to which Rosemary protests that the baby's eyes are nothing like those of Guy. It is then explained to Rosemary that Guy is actually not the child's real father; her newborn child, named Adrian, is actually the spawn of Satan, a fact which Rosemary is horrified to learn. Guy attempts to calm Rosemary by explaining to her that they will be generously rewarded with possible wealth and fame in exchange for having produced the Devil's offspring, and that they can conceive a second child that will truly be theirs. Rosemary takes no solace in Guy's words, instead responding by spitting in his face. Minnie tells Rosemary that she should be honored to be the "lucky" woman chosen to bear a child for Satan. Roman urges her to become a mother to her son, and assures her that she does not have to join the cult if she does not want to. She adjusts her son's blankets and gently rocks his cradle with a small smile on her face.
Where does the secret door that Rosemary finds lead to?
Into the Castevet apartment