Le Parisien newspaper reported that the man sprayed teargas in the young woman's face and then covered her in petrol on Saturday evening.
The father was apparently annoyed that the woman planned to go out with a group of friends that evening and considered her "too emancipated".
The newspaper quoted a source describing him as a "Muslim fundamentalist."
The 23-year-old daughter has a room in a building in the city's 11th arrondissement, close to the Place de la Bastille.
The 49-year-old man went there at around 11.30pm on Saturday evening and started arguing with her in the hall of the building.
He then attacked her with the teargas and poured petrol over her head and face, after which he pulled out a lighter, causing her to scream.
"She managed to grab the lighter from his hands while passers-by heard her screams," said a source close to the inquiry. "The man quickly made a run for it."
The woman told police her father had been harassing her for several weeks. "She explained he was unhappy that she had a Jewish boyfriend," said the source.
Police caught up with the man on Sunday and are questioning him in connection with attempted murder.
The newspaper reported that the man had only recently reconnected with his daughter, after abandoning her as a child.
He had recently taken her to his native country of Tunisia where he had tried to arrange a marriage for her.
She had resisted, while promising to behave in accordance with his wishes back in Paris.