While sketching a panther at the zoo, Serbian fashion artist Irena Dubrovna [Simone Simon] meets American Oliver Reed [Kent Smith]. She invites him to her apartment for tea. A few months later, they are married.
Irena is a strange and lonely woman with no friends. She has a fascination with panthers, but animals don't seem to like her very much. When Oliver brings her a Siamese kitten as a gift, for example, the cat hisses at Irena, so they return to the pet store and exchange it for a bird. While in the pet store, Irena's presence sets all the animals to caterwauling. Several weeks later, the bird dies in fear when Irena reaches for it in its cage.
Irena is haunted by a tale from her country that tells how the people of her village were witches, devil worshippers, and, under strong emotions like jealousy or anger, could change into panthers. She refers to them as the 'cat people.' Oliver takes it as a folktale, but Irena takes it for real, so real that she refuses to sleep with her husband because she believes that she might kill him.
Oliver suggests that Irena see a psychiatrist, so she goes to see Dr Louis Judd [Tom Conway], who was recommended to Oliver by his co-worker, Alice Moore [Jane Randolph]. When Irena returns home after the first session, she finds Oliver and Alice seated on the couch, talking about her. Irena gets angry when Oliver reveals that he has told Alice about her problem.
About a week later, Oliver runs into Dr Judd and learns that Irena has stopped seeing him. Concerned about Irena's belief in these folktales, Oliver again confides in Alice. Alice lets on that she's secretly in love with Oliver, and Oliver admits that he isn't so sure anymore that he really loves Irena. When Oliver gets home from work that evening, he and Irena quarrel about her not keeping her appointments with Dr Judd, so Oliver goes back to the office, stopping first at the snack shop around the corner. Irena calls the office, but when Alice answers the phone, she hangs up. When Alice learns from the cleaning lady that Oliver is in the snack shop, she decides to join him. Irena walks down to the office, passing the snack shop along the way and sees Oliver and Alice in there together. When they leave the shop, Irena follows Alice, scaring her badly.
One afternoon, Oliver, Irena, and Alice go to the museum. Oliver and Alice are interested in seeing the scale models of boats, and they suggest that Irena look at some other displays on the next floor rather than being bored by boats. They plan to meet in about an hour, but Irena does not show. After leaving the museum, Alice goes to the gymnasium for a late swim. Irena follows her. The place is empty, save for the desk clerk and cleaning lady. As Alice gets into her swimsuit, she hears what sounds like a growl. Scared, Alice dives into the deep end of the pool and treads water in place. The growling gets louder. It's in the pool room with her. Alice starts to scream. Suddenly the light goes on, revealing Irena standing there. Irena asks if Alice knows where Oliver is, and then leaves. When Alice gets out of the water, she finds that her robe has been torn to ribbons.
Alice goes to see Dr Judd. She tells him about being followed twice by something inhuman, which she believes may be Irena's cat form. Judd thinks it's all in her imagination. Irena consults Dr Judd, too. She tells him about the incidents with Alice, but he tells her that she is on the border of insanity and he could have her put away. He advises her to forget all this cat people stuff and lead a normal life. When Oliver comes home that evening, Irena is setting the table for a romantic dinner. She tells him that she's no longer afraid, but Oliver says that it's too late. 'I love Alice,' he admits. Irena tells him to leave. The next afternoon, Oliver and Alice have lunch with Dr Judd to discuss how to proceed with Irena. Dr Judd recommends an annulment so that they can marry, but Oliver and Alice opt to have Irena committed to a mental hospital where she can get the help she needs. They arrange for a meeting with Irena at 6 pm at her apartment.
It is now 7:30 pm, and Irena hasn't shown, so the three of them leave, Oliver and Alice intending to return to the office. Dr Judd walks out with them but then asks for the key to the apartment so that he can retrieve his cane, which he conveniently 'forgot'. What he really does is to leave the door unlocked. Oliver and Alice are working when the telephone rings. Alice answers, but the caller hangs up. Alice is scared and wants to leave. They turn out the lights and go to the door, but it is locked. Then they hear a growl and see a panther in the room with them. Oliver grabs a cross and tries talking to Irena, pleading with her to leave them alone. Oliver and Alice manage to get out of the building but not before smelling Irena's perfume.
Dr Judd has gone back to Irena's apartment. When she comes in, he tries to kiss her. Irena turns into a panther and kills him, but not before he stabs her with his cane. Irena goes to the zoo and unlocks the panther's cage with a key she stole from the zookeeper several days ago. The panther leaps at her, knocking her over and killing her. Oliver and Alice find Irena lying dead on the ground outside the panther's cage.
'She never lied to us,' Oliver says to Alice.
[Original synopsis by bj_kuehl.]