The film opens with a real estate agent showing a young newlywed couple around a seventh floor unit in an exclusive apartment building on the Upper West Side called The Bramford. Named Rosemary and Guy Woodhouse, the couple fall in love with the unit, but are puzzled to find a large secretary blocking the hall closet. Despite being warned by their friend Hutch that the building has a sordid past, the couple decides to move in anyway. Rosemary meets a woman named Terry Gionoffrio in the basement doing laundry, who tells Rosemary she is a guest of the Castevets, the Woodhouses' neighbors. Terry shows Rosemary a foul-smelling "Tannis charm" necklace given to her by Minnie Castevet. Rosemary and Guy later hear strange noises through the partition in the bedroom wall, and come home one evening to find that Terry Gionoffrio has committed suicide by leaping from a seventh story window.
Rosemary then has a strange dream blending the image of the broken window with memories from her Catholic upbringing. Minnie Castevet calls on Rosemary, introducing herself and inviting her and Guy over for a steak dinner. Rosemary and Guy reluctantly accept, not wanting to become overly familiar with the Castevets. Minnie's husband Roman compliments Guy's acting abilities, and reveals that he grew up in the theater world. Roman and Guy agree over dinner that all religions are merely "showbiz." Rosemary notices that pictures were missing from the Castevets' walls, and that they own lots of silver but only three matching plates. Despite mocking the Castevets, Guy tells Rosemary he has agreed to visit Roman the following day to hear more stories about the New York theater world.
One day, Minnie comes by with her friend Laura-Louise and gives Rosemary the same "Tannis root" charm worn by Terry Gionoffrio. Rosemary is unsettled, but accepts it out of politeness. Guy learns over the phone that an actor named Donald Baumgart with whom he was competing for a role has suddenly gone blind, opening up the part for Guy. Walking with her friend Hutch, Rosemary tries to downplay the ominous events that have transpired at The Bramford. Later, Guy apologizes to Rosemary for allowing himself to become consumed by his work, suggesting that they try to conceive. They share an evening in together, and Minnie brings by two chocolate mousses for them to eat for dessert. Rosemary remarks that hers has a "chalky undertaste," and ladles it into her napkin when Guy pressures her to eat it. She quickly becomes dizzy and faints in bed. She dreams Guy is undressing her on a yacht full of people, then imagines being lifted toward the Sistine Chapel. Naked coven members gather around her and paint her body, and a glamorous woman in white soothes her as her arms and legs are restrained to the bed. A naked Guy approaches, and then transforms into Satan before raping her. The last thing Rosemary sees is the Pope wearing the Tannis charm.
The next morning, Rosemary finds claw marks all over her body, and realizes Guy raped her while unconscious so as not to miss "baby night." She notices Guy no longer looks her in the eyes. Rosemary learns she is pregnant and tells Guy it should signal a "new beginning" for them. He convinces her to allow him to tell Minnie and Roman. Minnie persuades Rosemary to abandon her current doctor (Dr. Hill) and begin seeing a new one (Dr. Sapirstein). Dr. Sapirstein tells Rosemary not to read books or talk to friends, and instructs her to consume Minnie's vitamin mixtures instead of a normal regimen of pills. Rosemary cuts her hair short, displeasing Guy. She begins to rapidly lose weight and feel sharp pain, which Dr. Sapirstein tells her is just a "natural expansion of the pelvis." Hutch visits and is aghast at her appearance. Roman shows up as well, and Rosemary notices he has pierced ears. Hutch inspects the Tannis charm and says it looks more like a mold or fungus than a root. Roman leaves and Guy returns home, seemingly in a rush. Hutch then leaves without being able to find one of his gloves.
Hutch calls one night and arranges a meeting with Rosemary the following morning. When he never shows, Rosemary calls him from a pay phone, but reaches instead a woman named Grace Cardiff who tells her Hutch has fallen into a coma. By chance, Rosemary sees Minnie on the sidewalk, who ushers a frail Rosemary back to The Bramford. Rosemary and Guy attend a New Year's party at the Castevets', where Dr. Sapirstein continues to ignore her reports of pain and Roman makes a strange toast: "To 1966-- The Year One!" Rosemary decides she wants to throw a party and only invite their young friends, and stops taking Minnie's vitamin drinks. At the party, Rosemary's condition shocks her girlfriends, who corner her in the kitchen and urge her to reach back out to Dr. Hill. After the party, Rosemary's pain suddenly vanishes, and she resumes consuming Minnie's drinks. Hutch dies, and at his funeral, Grace Cardiff gives Rosemary a book he left her called "All them witches." She says Hutch told her to tell Rosemary, "The name is an anagram." Rosemary reads the book, which describes the Marcato family, and something called "Devil's Pepper" (a foul-smelling ingredient used in witchcraft rituals). Rosemary uses Scrabble letters to rearrange "Steven Marcato" into "Roman Castevet."
Rosemary tells Guy in a panic their neighbors are witches and that they must immediately move out. Guy dismisses her concerns and takes Hutch's book away from her. Dr. Sapirstein soothes Rosemary with reassurances, telling her Roman is terminally ill, and that he will convince Roman and Minnie to leave town earlier for a trip they were already planning to take to Dubrovnik. After Guy tells Rosemary he threw Hutch's book away, Rosemary drops her Tannis charm down a sewer drain and buys two more volumes on witchcraft, learning that witches need one of their victim's personal possessions before casting a spell. She calls Donald Baumgart and learns that Guy suggested that they exchange ties. Realizing Guy is a conspirator, Rosemary flees The Bramford and goes to see Dr. Sapirstein. When the receptionist there tells Rosemary that Dr. Sapirstein's aftershave smells exactly like her Tannis charm, Rosemary realizes that everyone around her is part of the plot. She calls Dr. Hill from a pay phone booth and manages to set up an appointment with him the following day. Thinking she is merely insane, Dr. Hill calls Guy and Dr. Sapirstein to collect Rosemary, who take her back to The Bramford. Rosemary manages to lock herself inside the apartment, but the coven still breaks in, and Dr. Sapirstein sedates her with a syringe as she begins to go into labor.
Upon waking, Guy tells Rosemary it's a boy. She sleeps and wakes again, finding Laura-Louise watching over her. Laura-Louise fetches Guy and Dr. Sapirstein, who tells Rosemary the baby died due to an ectopic birth. Rosemary accuses them of being witches and stealing her baby, and Dr. Sapirstein sedates her once more. Waking up again, Rosemary sees Guy, who tells her she had "pre-partum crazies," and gives her a pill to take. Rosemary demands that he show her his arms, thinking they will bear a satanic marking, but they are clean. Rosemary begins stashing her pills in her bed-frame and hears a baby crying through the walls, which Guy says belongs to a couple "up on eight." Laura-Louise forces Rosemary to pump breast-milk. Left alone one night, Rosemary discovers a secret passage in the hall closet linking the Woodhouse and Castevet apartments. She wanders through and finds the entire coven gathered around a black bassinet. She looks into it and wildly cries, "What have you done to its eyes?" Roman explains that Satan, not Guy, is the baby's father, and that his name is Adrian. Guy tells Rosemary they can still have a child of their own, and that his exploding career will soon deliver them wealth and fame. Roman tries to persuade Rosemary into becoming the child's mother by saying Minnie and Laura-Louise are too old for the job. Rosemary slowly approaches the bassinet and begins to rock it, as a Japanese man takes photographs. The child's lullaby that opened the film begins to play once more.