"The executive board has been briefed on that matter, including this year, and continues to express its confidence in the managing director's ability to effectively carry out her duties," said spokesman Gerry Rice.
Lagarde was questioned on January 31 by French investigators in a special court for cases involving ministers for her role in a 400 million euro (USD 540 million) state payout made to tycoon Bernard Tapie in 2008.
Lagarde was France's economy minister at the time the payout was being decided.
The payout was connected to a dispute between the businessman and partly state-owned bank Credit Lyonnais over his 1993 sale of sportswear group Adidas.