It was not immediately clear what the slogan meant.
Police detained her and on Friday the museum said it was temporarily closing the wing of the museum in which the painting was being displayed.
The Louvre said in a statement that a specialist art restorer was being sent to the site but that it believed the damage was not significant and could be easily repaired.
A prosecutor in the nearby town of Bethune who is handling the case said he had asked for a psychiatric evaluation of the young woman who he said appeared to be "unbalanced".
He said her reasons for defacing the painting were not yet clear.
The painting by Delacroix 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.