Anton Rüsch, the prosecutor in charge of the case, announced on Saturday that a 21-year-old Swiss woman was arrested in the connection with the January 20th fire.
This followed the arrest on Thursday of another 21-year-old woman, originally from Kosovo, who has admitted to her involvement.
The two woman face charges of arson and theft.
Video surveillance cameras, installed in the square outside the library last fall, enabled investigators to track down the Kosovar, Le Matin Dimanche reported on Sunday.
The woman, already known to police for multiple infractions, including thefts and robberies, was identified by an officer viewing the videotape, the newspaper said.
In an interview with Rüsch, the woman reportedly admitted to breaking into a library office, without reason.
The woman noticed a safe in the office but was unable to open it, Le Matin Dimanche said.
She explained that she collected paper and set fire to it, on the spur of the moment fand or no particular reason, the newspaper said.
No information from the second woman arrested was immediately made public.
The fire destroyed two offices and damaged 100,000 books, which need to be cleaned from soot and smoke.
The head of the library, Frédéric Sardet, initially said the library would be closed to the public for a week.
However, it now appears it will not reopen for at least a further 10 days because of the work needed to clean the books.
Officials expect it will take several months before the offices can be rebuilt.