The museum said that Anne Baldassari's departure today came after a meeting with the country's culture minister.
Renovations at the museum have dragged for five years amid accusations of mismanagement, labour problems and clashes between the artist's family and the French government. The reopening has now been pushed back until September after the summer tourist season.
Claude Picasso, the painter's son, lashed out this month, saying he had the impression France "doesn't care" about him or his father.