Irena Gallier (Natassia Kinski) is a young woman whom was raised by adoptive parents and is, for the first time since childhood, meeting her older brother Paul living in New Orleans. Paul (Malcolm McDowell) meets Irene when she arrives at the airport and drives her home to his apartment. Paul lives by himself with only his housekeeper Female (pronounced Fee-MAL-ee) (Ruby Dee) to look after him. Irena and Paul are descended from a line of 'cat people,' people who turn into panthers after mating and who must then kill in order to take human form again. Irena knows nothing about this side of her ancestry. She is still a virgin, so she has no idea what sex will do to her. On the other hand, Paul has been living with this knowledge for years and has worked out a system whereby he uses hookers as his prey.
In fact, on Irena's first night in New Orleans, Paul arranges for a hooker (Lynn Lowry) to meet with him at a cheap hotel. Unfortunately (for Paul) but fortunately (for the hooker), the hooker escapes with her life and Paul is left in his panther form, trapped in a hotel room. Curator Oliver Yates (John Heard) and his assistants, Alice Perrin (Annette O'Toole) and Joe Creigh (Ed Begley Jr), from the New Orleans Zoo, are called to capture the black panther and put him behind bars. With Paul gone, Irena decides to spend her first full day in New Orleans by seeing the sights.
First, a taxi ride through the French Quarter; then a stop at the zoo where she is fascinated by the new panther, so fascinated that she is still there sketching him 1-1/2 hours after the zoo has closed. When Oliver startles Irena, she drops her sketch pad and runs for the trees, winding up on top of one. Oliver coaxes her down. After noticing that Irena feels excessively warm, Oliver takes her inside and puts a cool cloth on her forehead. Thinking her exhaustion might be due to hunger, they decide to get something to eat. During the dinner conversation, Oliver learns that Irena is looking for a job and hires her to work in the zoo's gift shop. Irena's first day on the job is memorable.
Alice introduces herself to Irena, and the two get lunch. A strange woman calls Irena 'mi hermana' (my sister). That afternoon, as Irena continues looking at the black panther, it suddenly goes crazy and when Joe tries subduing it, the panther graphically rips Joe's right arm off and he quickly bleeds to death. By the time Oliver gets back with his gun to kill the beast, however, the panther has disappeared. When Irena gets home that evening, Paul returns, but he no longer seems so brotherly. He claims that he was "in jail" during his time away. He tries to get Irena to have sex with him, telling her that he's the only one who can touch her and she's the only one who can touch him.
Irena knows only that she is attracted to Oliver and wants nothing to do with having sex with her brother, so she runs off. While running in the street, Irena flags down a police car, but they find no one chasing her. However, when the police dog begins going nuts, they do a search of the area. The police dog leads them to Paul's basement where they find a cage, chains, and parts of several bodies. A check on Paul Gallier shows that he's been in and out of mental institutions since the age of 10, when his parents killed themselves.
They were circus performers, and Paul grew up around big cats. Thinking that Paul might have been the one keeping the escaped panther, they call the Zoo. Oliver and Alice come over. It is the policeman's opinion that Paul meant to kill Irena, so he suggests that she find someplace else to live. Oliver offers her a place to stay with him. Irena is becoming more and more troubled.
As if the stuff with Paul wasn't bad enough, one night she finds herself running on all fours after a rabbit. It's also becoming apparent to her that she is falling in love with Oliver, and he with her, but she tells him that she cannot make love to him. Alice is also in love with Oliver, and this is evoking feelings of rivalry in Irena. A week goes by, and the search for the escaped panther has proven fruitless. In the meantime, Paul has murdered another girl. He feels that he can no longer go on like this.
He crashes through Irena's bedroom window one night and, once more, tries to have sex with her. It's the only way they can live, he explains, just as their parents, who were also brother and sister, lived together as husband and wife. Irena refuses and stabs him with a piece of broken window glass. Paul turns into a panther. When Oliver comes home, Alice in tow, he is attacked by the panther. Alice gets the shotgun and shoots it dead.
When Oliver autopsies the panther, he is horrified to see a human hand in its stomach, after which the entire panther spontaneously disintegrates. The next morning, Alice is out jogging. It's getting late, and she stops at the gym for a quick swim and change of clothes. As she is getting undressed, she hears a growl. Afraid, Alice jumps into the pool. Suddenly, the lights go out and the growling gets louder. Alice begins to scream.
When the lights are turned back on, Irena is standing there. The receptionist hands Alice her robe, only to find that it is torn into shreds. Alice calls Oliver to warn him of her experience, but Oliver is too charmed by Irena, who has just returned and is taking off her clothes, letting him know that she is ready to make love. Afterwards, she turns into a panther, but she leaves before she can harm Oliver. She is spotted near the bridge. SWAT teams have been called to corner the panther.
Oliver and Alice arrive. Despite this presence, the panther gets away. Oliver goes looking for Irena. He finds her in human form because she has killed. Irena begs Oliver to kill her. Oliver refuses, so Irena asks him to free her by making love once more. "I want to live with my own" she says.
Oliver binds her arms and legs to the bed, strips off all of her clothes, and makes love to her. In the final scene, Oliver stops at the new panther's cage at the zoo. It is obvious that the "re-captured panther" is Irena, now trapped forever in her panther form. Oliver reaches through the bars and strokes the docile panther's neck..