Her lawyer Yves Repiquet said Ms Lagarde, who this week was questioned in Paris for a fourth time under her existing status as a witness in the long-running saga, said the negligence allegation was unfounded.
He said they planned to appeal the move and added that Ms Lagarde had no plans to resign.
In French law, magistrates place someone under formal investigation when they believe there are indications of wrongdoing, but that does not always lead to a trial.
The inquiry relates to allegations tycoon Bernard Tapie, a supporter of conservative former president Nicolas Sarkozy, was improperly awarded hundreds of million of euros to settle a dispute with the now defunct, state-owned bank Credit Lyonnais.
The inquiry has already involved several of Mr Sarkozy's cabinet members and France Telecom CEO Stephane Richard, who was an aide to Ms Lagarde when she was Mr Sarkozy's finance minister.
Ms Lagarde has accused Mr Richard of having used her pre-printed signature to sign off on a document facilitating the payment, but he says she was fully aware of the move.