"As we have said before, it would not be appropriate to comment on a case that has been and is currently before the French judiciary," it said in a statement.
"The Executive Board has been briefed on recent developments related to this matter, and continues to express its confidence in the managing director's ability to effectively carry out her duties."
A Paris court placed Lagarde under formal investigation earlier this week for alleged "negligence" in a 2008 graft case dating back to when she was a French finance minister.
In France, being placed under formal investigation is the nearest equivalent to being charged, and occurs when an examining magistrate decides there is a case to be answered.
The judge may eventually decide to remove Lagarde from being under investigation, and she would not face prosecution.
But the action was a serious development for Lagarde, whose previous status was as a special witness in the long-running French probe.
Lagarde plans to appeal the court decision which she called "totally without merit". She said that she had no intention of resigning her Fund post.
The negligence allegation relates to her handling of a 400-million-euro ($527 million) state payout to disgraced French tycoon Bernard Tapie in 2008.
Lagarde referred the dispute between Tapie and partly state-owned bank Credit Lyonnais to a three-member arbitration panel that ruled in favor of Tapie and ordered the payout.
Lagarde's predecessor, French politician Dominique Strauss-Kahn, was forced to resign in 2011 following accusations he sexually assaulted a hotel maid in New York.