The suspect was arrested in a western suburb of the capital, a police official said, and his flat was searched for four hours late Friday. An AFP journalist saw the man being led out handcuffed with his head covered.
The 19-year-old victim, named as Susanna Zetterberg, 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, with four bullets in the head. She had also been knifed.
There was no trace of sexual assault but officials believe the killer may have set fire to the body to destroy evidence.
The man, who posed as a taxi driver, was seen shortly before his arrest “digging up or, more likely, burying something in the bois de Boulogne,” a huge wooded area in the west of Paris, an investigator said, adding that police were “90 percent sure” of having caught their man after a “race against the clock”.
The victim had gone to a nightclub on Friday and after taking a taxi at 4 am sent a text message to a French friend saying the driver “doesn’t look nice.”
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.