The case involves the 2007 settlement of a lawsuit between billionaire Bernard Tapie and a state-run bank, Credit Lyonnais.
The dispute concerned the 1993 sale of sports group Adidas, Radio France Internationale reported Thursday.
In 2007, while she was the French finance minister, Lagarde intervened by ordering the prolonged legal dispute to go to arbitration. That resulted in the bank paying Tapie a $522.7 million settlement.
Prosecutors have called the process "questionable." It is suspected that sending the case to arbitration was a payback for Tapie's support of former French President Nicolas Sarkozy, the report said.
As the bank is state-owned, interfering with the case that resulted in a settlement could be considered a misuse of state funds.
Lagarde's attorney Yves Repiquet said the summons "has been expected for several months."
Repiquet called the summons a "non-event."
The case was filed at the Court of Justice of the Republic, a special court that deals with high-level political cases.