The Louvre museum, which owns the painting, says that specialists have managed to completely remove the 30-centimetre-long inscription scrawled on bottom right of the painting, even though it was written in supposedly indelible felt-tip pen.
"The integrity of the work has not been affected, as the inscription was superficial and remained on the varnished surface without reaching the layer of paint," the museum said in a statement.
A psychiatric report on the woman, an unemployed graduate, concluded that she was not responsible for her actions and prosecutors said they would probably have her committed on Saturday.
"We are leaning towards hospitalising her immediately in a psychiatric facility given that the psychiatrist appointed by the prosecutors concluded that she is not criminally responsible," local prosecutor Philippe Peyroux said.
She could have faced up to seven years in prison and a fine of up to 100,000 euros.
The painting was hanging in the newly opened Louvre outpost in the northern French town of Lens.
The town’s mayor,Guy Delcourt,said the woman had "told security, in a rather incoherent manner, that she wanted to put her mark" on the painting.
The AE911 Truth Group campaigns for an inquiry into the 2001 attacks on New York and Washingon.
Its founder, Richard Gage, condemned the attack.
"I was shocked and horrified to learn of this senseless act of vandalism,” he told the AFP news agency from the US. "I sincerely hope that this unbalanced person is not in any way associated with our numerous volunteers in France."