The incident occurred just before closing time at the new branch of the Louvre in Lens, northern France, which was opened in December last year by President François Hollande.
The 28-year-old, who is believed to suffer from psychological problems, used a black marker to scrawl a 30cm long scribble "AE911" on the art work, the flagship painting of the Lens-Louvre gallery.
According to reports on France's TF1 on Friday the tag refers to the 9/11 terrorist attacks in New York. TF1 claim the "AE" stands for "Architect and Engineer", a group who believe in the conspiracy theory that the twin towers were destroyed not by planes but by explosives.
She made the mark in the bottom right hand corner of the painting before security staff and members of the public were able to apprehend her.
The museum has filed a complaint to police and the Ministry of Culture in Paris have demanded an investigation.
Thankfully, gallery bosses are positive the work can be restored.
"This incident will not effect our plans to display more of the Louvre's works at its Lens gallery," a statement from the Paris museum read on Thursday.
Delacroix's renowned painting was hung in the central hall of the exhibition and was used for the marketing campaign to publicize last year's launch. It was replicated on a giant billboard hanging in Paris's Gare du Nord train station.
The painting commemorates France's July Revolution of 1830. It shows a bare-breasted woman personifying Liberty leading the people forward over the bodies of the fallen, holding the French tricolour in one hand and a bayonetted musket in the other.
On Friday, bosses at the museum, said they had managed to remove the AE911 tag without any damage to the painting.