The suspect was arrested in a western suburb of the capital, a police official said.
The 19-year-old victim, named only as Susanna, went missing on her way home from a Paris nightclub last Friday.
Her body, handcuffed and partly burned, was found the following day in a forest in Chantilly, north of the capital.
There was no trace of sexual assault but officials believe the killer may have set fire to the body to destroy evidence.
Investigators have been looking into a connection with an attack in February in which another Swedish woman was raped on her taxi ride home, then pushed out of the car in a forest west of Paris.