French magistrates earlier this week put Lagarde under formal investigation for "negligence" after questioning her in Paris for a fourth time. The long-running saga concerns allegations that tycoon Bernard Tapie won a large arbitration payout due to political connections when Lagarde was French finance minister.
"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," the board said in a statement.
The 24-member board, which has the power to hire and fire the IMF's managing director, discussed the French corruption probe after the first three times Lagarde was questioned under her previous status as a witness, and also considered the case's implications when it decided to hire her in 2011.
Three sources told Reuters on Thursday the board would likely stand behind Lagarde this time, as well.
Lagarde's lawyer said he would appeal the decision to move to an investigation, and the legal appeals process would likely last beyond the end of Lagarde's first five-year IMF term, which ends in July 2016.
In the case, Lagarde is accused of "negligence" for not blocking the arbitration that won Tapie a huge pay-out. She has said the case is "without merit."
Under French law, magistrates place a person under formal investigation when they believe there are indications of wrongdoing, but that does not always lead to a trial.