During the events of the preceding film Beneath the Planet of the Apes, occurring off-screen, Cornelius (Roddy McDowall) and Zira (Kim Hunter) escaped Earth prior to its destruction when they accompanied their fellow chimpanzee Dr. Milo (Sal Mineo) in salvaging and repairing the spaceship originally used by Taylor. The shock wave of Earth’s destruction sends the ship through a time warp that brings the apes to 1973 Earth, splashing down off the Pacific coast of the United States. (The backward time travel of the apes creates a time paradox which is a key element of the plot in the confrontation between the apes and Dr. Otto Hasslein: is it possible for the apes or humans in 1973 to alter the future where the apes have come from? Can the future dominance of apes be prevented from happening?)
The apes are transported to a secluded ward of the Los Angeles Zoo, under the observation of scientists Dr. Stephanie Branton (Natalie Trundy) and Dr. Lewis Dixon (Bradford Dillman). With Dr. Milo explaining their situation in private, the apes decide not to let the humans know that they can speak while agreeing not to reveal Earth’s destruction from the Ape War. However Zira’s impatience exposes the apes’ power of speech during an experiment and Dr. Milo is killed moments later by a zoo gorilla who became agitated by the chimpanzees’ argument. Lewis tries to communicate with the apes that he is peaceful and he wishes to treat them as equals, winning their friendship as a result.
A Presidential Commission is formed to investigate the return of Taylor’s spaceship and determine how atypically intelligent apes came to be aboard it. The apes are brought before the Commission, where they publicly reveal their ability to speak. The council asks them about Taylor, but Cornelius and Zira tell them that they know nothing about him. They reveal that they came from the future and escaped Earth when war broke out. They are welcomed as guests of the government. Cornelius and Zira secretly tell Stephanie and Lewis that they did know about Taylor, explain how humans are treated in the ape-dominated future, and about the Earth’s destruction. Stephanie and Lewis are shocked but still sympathetic, the latter advising the couple to keep this information secret until they can gauge the potential reaction of their hosts.
The apes become celebrities, and are lavished with gifts and media attention. They come to the attention of the President’s Science Advisor Dr. Otto Hasslein (Eric Braeden), who discovers Zira is pregnant. Fearing for the future of the human race, he offers her champagne (for which she has developed a taste) to loosen her inhibitions and questions her further while recording it. Her candid responses enable him to convince the Commission that Cornelius and Zira must be subjected to more rigorous questioning.
Hasslein insists that he simply wants to know how apes became dominant over men. Cornelius reveals that the human race will cause its own downfall and become dominated by simians, and that simian aggression against humans will lead to Earth’s destruction by a weapon made by humans. Zira explains that the gorillas started the war, and the orangutans supported the gorillas, but the chimpanzees had nothing to do with it. Hasslein suspects that the apes are not speaking the whole truth.
During the original hearing, Zira had accidentally revealed that she dissected humans in the course of her work. Hasslein orders Lewis to administer a truth serum to her while Cornelius is confined elsewhere. Lewis assures Zira that the serum will have the same effect as champagne. As a result of the serum, Hasslein learns details about Zira’s examination and experimentation on humans along with her knowledge of Taylor.
Zira joins Cornelius in confinement while Hasslein takes his findings to the President (William Windom), who reluctantly must abide by the council’s ruling to have Zira’s pregnancy be terminated and that both apes be sterilized. In their chambers, Cornelius labels Hasslein and the others savages for Zira’s treatment as she reminds Cornelius that she did the same thing to humans and Taylor called them savages. Zira is relieved to have revealed the truth because she was tired of lying. Cornelius fears that the truth will get them killed. When an orderly arrives to offer the apes food, his playful reference to their unborn child as a “little monkey” makes Cornelius lose his temper and he knocks the orderly to the floor, before escaping with Zira. Cornelius assumes he merely knocked out the orderly, but he is actually dead. Hasslein uses the tragedy in support of his claim that the apes are a threat and calls for their execution, but is ordered by the President to bring them in alive as he will not endorse punishment for the orderly’s death until due process has been served.
Branton and Dixon help the apes to escape, taking them to a circus run by Señor Armando (Ricardo Montalbán), where an ape named Heloise has just given birth. Zira gives birth to a son, whom she names Milo in honor of their deceased friend. When Hasslein, knowing that Zira’s labor was imminent, orders a search of all circuses and zoos, Armando insists the apes leave for their safety. Lewis arranges for the apes to hide out in the shipyard in the Los Angeles harbor until the coast is clear to return to the circus as it heads to Florida, giving Cornelius a pistol as the couple do not want to be taken alive.
Hasslein tracks the apes to the shipping yard and mortally wounds Zira when she refuses to hand over the infant, firing several shots into the infant before being killed by Cornelius. Cornelius is shot by a sniper and falls, Zira tossing the dead baby over the side and crawling to die with her husband, witnessed by a grieving Lewis and Stephanie.
As Armando’s circus prepares to leave for Florida, it is revealed that Zira switched babies with Heloise prior to leaving the circus and that Armando is aware of this. Milo begins to talk.