The Court of Justice of the Republic ordered the investigation Thursday into allegations that Lagarde abused her power in a 2007 dispute involving a multimillion-dollar payout to a French tycoon.
Legal experts told The New York Times the investigation likely wouldn't interfere with her management of the IMF.
"She should be able to continue her duties with no problem because the IMF was made aware of this potential investigation when she submitted her candidature and they voted for her nonetheless," said Christopher Mesnooh, a partner with Field Fisher Waterhouse in Paris.
The fund's board said in a statement it was confident Lagarde "will be able to effectively carry out her duties."
Lagarde was appointed IMF managing director in June, replacing Dominique Strauss-Kahn, who stepped after being charged with sexually abusing a hotel maid in New York.